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15 pages, 295 KiB

Open AccessArticle

k-Almost Newton-Conformal Ricci Solitons on Hypersurfaces Within Golden Riemannian Manifolds with Constant Golden Sectional Curvature

by Amit Kumar Rai, Majid Ali Choudhary, Mohd. Danish Siddiqi, Ghodratallah Fasihi-Ramandi, Uday Chand De and Ion Mihai

Axioms 2025, 14(8), 579; https://doi.org/10.3390/axioms14080579 - 26 Jul 2025

Viewed by 248

Abstract

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions [...] Read more.

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)

16 pages, 271 KiB

Open AccessArticle

On Ricci Solitons and Curvature Properties of Doubly Warped Products with QSMC

by Md Aquib, Vaishali Sah, Sarvesh Kumar Yadav and Jaya Upreti

Axioms 2025, 14(8), 548; https://doi.org/10.3390/axioms14080548 - 22 Jul 2025

Viewed by 156

Abstract

This paper explores the geometric interplay between the Levi–Civita connection and the quarter-symmetric metric connection on doubly warped product manifolds. We analyze the behavior of Ricci solitons on such manifolds, focusing on the influence of conformal and Killing vector fields within the framework [...] Read more.

This paper explores the geometric interplay between the Levi–Civita connection and the quarter-symmetric metric connection on doubly warped product manifolds. We analyze the behavior of Ricci solitons on such manifolds, focusing on the influence of conformal and Killing vector fields within the framework of quarter-symmetric metric connections (QSMCs). Furthermore, we examine conditions under which the manifold exhibits Einstein properties, presenting new insights into Einstein-like structures in the context of doubly warped product manifolds endowed with a quarter-symmetric metric connection. Full article

(This article belongs to the Special Issue Recent Developments in Differential Geometry and Its Applications)

12 pages, 277 KiB

Open AccessArticle

Pair of Associated η-Ricci–Bourguignon Almost Solitons with Generalized Conformal Killing Potential on Sasaki-like Almost Contact Complex Riemannian Manifolds

by Mancho Manev

Mathematics 2025, 13(13), 2165; https://doi.org/10.3390/math13132165 - 2 Jul 2025

Viewed by 178

Abstract

The subject of this study is almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds. The considerations are restricted to a special class of these manifolds, namely those of the Sasaki-like type, because of their geometric construction and the explicit [...] Read more.

The subject of this study is almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds. The considerations are restricted to a special class of these manifolds, namely those of the Sasaki-like type, because of their geometric construction and the explicit expression of their classification tensor by the pair of B-metrics. Here, each of the two B-metrics is considered as an

η

-Ricci–Bourguignon almost soliton, where

η

is the contact form. The soliton potential is chosen to be a conformal Killing vector field (in particular, concircular or concurrent) and then a generalization of the notion of conformality using contact conformal transformations of B-metrics. The resulting manifolds, equipped with the introduced almost solitons, are geometrically characterized. In the five-dimensional case, an explicit example on a Lie group depending on two real parameters is constructed, and the properties obtained in the theoretical part are confirmed. Full article

(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

12 pages, 233 KiB

Open AccessArticle

Rigidity Characterizations of Conformal Solitons

by Junsheng Gong and Jiancheng Liu

Mathematics 2025, 13(11), 1837; https://doi.org/10.3390/math13111837 - 31 May 2025

Viewed by 303

Abstract

We study the rigidity of conformal solitons, give a sufficient and necessary condition that guarantees that every closed conformal soliton is gradient conformal soliton, and prove that complete conformal solitons with a nonpositive Ricci curvature must be trivial under an integral condition. In [...] Read more.

We study the rigidity of conformal solitons, give a sufficient and necessary condition that guarantees that every closed conformal soliton is gradient conformal soliton, and prove that complete conformal solitons with a nonpositive Ricci curvature must be trivial under an integral condition. In particular, by using a p-harmonic map from a complete gradient conformal soliton in a smooth Riemannian manifold, we classify complete noncompact nontrivial gradient conformal solitons under some suitable conditions, and similar results are given for gradient Yamabe solitons and gradient k-Yamabe solitons. Full article

(This article belongs to the Section B: Geometry and Topology)

6 pages, 177 KiB

Open AccessEditorial

Differentiable Manifolds and Geometric Structures

by Adara M. Blaga

Mathematics 2025, 13(7), 1082; https://doi.org/10.3390/math13071082 - 26 Mar 2025

Viewed by 428

Abstract

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the [...] Read more.

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in different areas of differential geometry, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as Golden space forms, Sasakian space forms; diffeological and affine connection spaces; Weingarten and Delaunay surfaces; Chen-type inequalities for submanifolds; statistical submersions; manifolds endowed with different geometric structures (Sasakian, weak nearly Sasakian, weak nearly cosymplectic, LP-Kenmotsu, paraquaternionic); solitons (almost Ricci solitons, almost Ricci–Bourguignon solitons, gradient r-almost Newton–Ricci–Yamabe solitons, statistical solitons, solitons with semi-symmetric connections); vector fields (projective, conformal, Killing, 2-Killing) [...] Full article

(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)

15 pages, 368 KiB

Open AccessArticle

Modified F(R,T)-Gravity Model Coupled with Magnetized Strange Quark Matter Fluid

by Mohd Danish Siddiqi, Meraj Ali Khan and Ibrahim Al-Dayel

Mathematics 2025, 13(4), 586; https://doi.org/10.3390/math13040586 - 10 Feb 2025

Viewed by 751

Abstract

This research note presents the properties of the

F (R, T)

-gravity model in combination with magnetized strange quark matter. We obtain the equation of state for the magnetized strange quark matter in the

F (R, T)

[...] Read more.

This research note presents the properties of the

F (R, T)

-gravity model in combination with magnetized strange quark matter. We obtain the equation of state for the magnetized strange quark matter in the

F (R, T)

-gravity model endowed with the Lagrangian through of Ricci curvature. We also examine the Ricci solitons supported by a time-like conformal vector field in

F (R, T)

-gravity, attached with magnetized strange quark matter fluid. Within this ongoing research, we give an estimate of the total quark pressure and total density in the phantom barrier and the radiation epochs of the Universe. Finally, using Ricci solitons, we study the various energy conditions, some black holes criteria, and Penrose’s singularity theorem for magnetized strange quark matter fluid spacetime coupled with the

F (R, T)

-gravity model. Full article

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)

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12 pages, 271 KiB

Open AccessArticle

A Conformal η-Ricci Soliton on a Four-Dimensional Lorentzian Para-Sasakian Manifold

by Yanlin Li, Arup Kumar Mallick, Arindam Bhattacharyya and Mića S. Stanković

Axioms 2024, 13(11), 753; https://doi.org/10.3390/axioms13110753 - 31 Oct 2024

Cited by 11 | Viewed by 874

Abstract

This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of [...] Read more.

This paper focuses on some geometrical and physical properties of a conformal η-Ricci soliton (Cη-RS) on a four-dimension Lorentzian Para-Sasakian (LP-S) manifold. The first section presents an introduction to Cη-RS on LP-S manifolds, followed by a discussion of preliminary ideas about the LP-Sasakian manifold. In the subsequent sections, we establish several results pertaining to four-dimension LP-S manifolds that exhibit Cη-RS. Additionally, we consider certain conditions associated with Cη-RS on four-dimension LP-S manifolds. Besides these geometrical points of view, we consider this soliton in a perfect fluid spacetime and obtain some interesting physical properties. Finally, we present a case study of a Cη-RS on a four-dimension LP-S manifold. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Mathematical Physics)

12 pages, 316 KiB

Open AccessArticle

Modified

F (R, T^{2})

-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

by Mohd Danish Siddiqi and Fatemah Mofarreh

Axioms 2024, 13(10), 708; https://doi.org/10.3390/axioms13100708 - 14 Oct 2024

Cited by 1 | Viewed by 965

Abstract

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity [...] Read more.

In the present research note, we discuss the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the

F (R, T^{2})

-gravity model. Furthermore, we deal with the energy–momentum squared gravity model

F (R, T^{2})

coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to

F (R, T^{2})

-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential

U_{n}

with hyperbolic Ricci solitons in the

F (R, T^{2})

-gravity model coupled with perfect fluid and a phantom barrier. Full article

21 pages, 324 KiB

Open AccessArticle

(Almost) Ricci Solitons in Lorentzian–Sasakian Hom-Lie Groups

by Esmaeil Peyghan, Leila Nourmohammadifar, Akram Ali and Ion Mihai

Axioms 2024, 13(10), 693; https://doi.org/10.3390/axioms13100693 - 4 Oct 2024

Viewed by 775

Abstract

We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional

sl (2, R)

and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is [...] Read more.

We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional

sl (2, R)

and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is a contact 1-form, conditions under which the Ricci curvature tensor is v-parallel are given. Ricci solitons for Lorentzian–Sasakian Hom-Lie algebras are also studied. It is shown that a Ricci soliton vector field

ζ

is conformal whenever the Lorentzian–Sasakian Hom-Lie algebra is Ricci semisymmetric. To illustrate the use of the theory, a two-parameter family of three-dimensional Lorentzian–Sasakian Hom-Lie algebras which are not Lie algebras is given and their Ricci solitons are computed. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)

16 pages, 284 KiB

Open AccessArticle

Exploring Conformal Soliton Structures in Tangent Bundles with Ricci-Quarter Symmetric Metric Connections

by Yanlin Li, Aydin Gezer and Erkan Karakas

Mathematics 2024, 12(13), 2101; https://doi.org/10.3390/math12132101 - 4 Jul 2024

Cited by 10 | Viewed by 964

Abstract

In this study, we investigate the tangent bundle

T M

of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection

\tilde{\nabla}

. Our primary goal is to establish the necessary and sufficient conditions for

T M

to exhibit [...] Read more.

In this study, we investigate the tangent bundle

T M

of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection

\tilde{\nabla}

. Our primary goal is to establish the necessary and sufficient conditions for

T M

to exhibit characteristics of various solitons, specifically conformal Yamabe solitons, gradient conformal Yamabe solitons, conformal Ricci solitons, and gradient conformal Ricci solitons. We determine that for

T M

to be a conformal Yamabe soliton, the potential vector field must satisfy certain conditions when lifted vertically, horizontally, or completely from M to

T M

, alongside specific constraints on the conformal factor

λ

and the geometric properties of M. For gradient conformal Yamabe solitons, the conditions involve

λ

and the Hessian of the potential function. Similarly, for

T M

to be a conformal Ricci soliton, we identify conditions involving the lift of the potential vector field, the value of

λ

, and the curvature properties of M. For gradient conformal Ricci solitons, the criteria include the Hessian of the potential function and the Ricci curvature of M. These results enhance the understanding of the geometric properties of tangent bundles under Ricci-quarter symmetric metric connections and provide insights into their transition into various soliton states, contributing significantly to the field of differential geometry. Full article

(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)

10 pages, 251 KiB

Open AccessArticle

Ricci Solitons on Spacelike Hypersurfaces of Generalized Robertson–Walker Spacetimes

by Norah Alshehri and Mohammed Guediri

Symmetry 2024, 16(5), 601; https://doi.org/10.3390/sym16050601 - 13 May 2024

Cited by 1 | Viewed by 1072

Abstract

In this paper, we investigate Ricci solitons on spacelike hypersurfaces in a special Lorentzian warped product manifold, the so-called generalized Robertson–Walker (GRW) spacetimes. Such spacetimes admit a natural form of symmetry which is represented by the conformal vector field

f \partial t

, [...] Read more.

In this paper, we investigate Ricci solitons on spacelike hypersurfaces in a special Lorentzian warped product manifold, the so-called generalized Robertson–Walker (GRW) spacetimes. Such spacetimes admit a natural form of symmetry which is represented by the conformal vector field

f \partial t

, where f is the warping function and

\partial t

is the unit timelike vector field tangent to the base (which is here a one-dimensional manifold). We use this symmetry to introduce some fundamental formulas related to the Ricci soliton structures and the Ricci curvature of the fiber, the warping function, and the shape operator of the immersion. We investigate different rigidity results for Ricci solitons on the slices, in addition to the totally umbilical spacelike supersurfaces of GRW. Furthermore, our study is focused on significant GRW spacetimes such as Einstein GRW spacetimes and those which obey the well-known null convergence condition (NCC). Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 3rd Edition)

18 pages, 293 KiB

Open AccessArticle

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

by Lixu Yan, Yanlin Li, Lokman Bilen and Aydın Gezer

Mathematics 2024, 12(9), 1395; https://doi.org/10.3390/math12091395 - 2 May 2024

Cited by 3 | Viewed by 1463

Abstract

Let

(M, \nabla, g)

be a statistical manifold and

T M

be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of [...] Read more.

Let

(M, \nabla, g)

be a statistical manifold and

T M

be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle

T M

. The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle

T M

according to the twisted Sasaki metric G. Full article

(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)

8 pages, 230 KiB

Open AccessArticle

Gradient Ricci Solitons on Spacelike Hypersurfaces of Lorentzian Manifolds Admitting a Closed Conformal Timelike Vector Field

by Norah Alshehri and Mohammed Guediri

Mathematics 2024, 12(6), 842; https://doi.org/10.3390/math12060842 - 13 Mar 2024

Cited by 1 | Viewed by 1023

Abstract

In this article, we investigate Ricci solitons occurring on spacelike hypersurfaces of Einstein Lorentzian manifolds. We give the necessary and sufficient conditions for a spacelike hypersurface of a Lorentzian manifold, equipped with a closed conformal timelike vector field

\bar{ξ}

, to be [...] Read more.

In this article, we investigate Ricci solitons occurring on spacelike hypersurfaces of Einstein Lorentzian manifolds. We give the necessary and sufficient conditions for a spacelike hypersurface of a Lorentzian manifold, equipped with a closed conformal timelike vector field

\bar{ξ}

, to be a gradient Ricci soliton having its potential function as the inner product of

\bar{ξ}

and the timelike unit normal vector field to the hypersurface. Moreover, when the ambient manifold is Einstein and the hypersurface is compact, we establish that, under certain straightforward conditions, the hypersurface is an extrinsic sphere, that is, a totally umbilical hypersurface with a non-zero constant mean curvature. In particular, if the ambient Lorentzian manifold has a constant sectional curvature, we show that the compact spacelike hypersurface is essentially a round sphere. Full article

(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)

16 pages, 295 KiB

Open AccessArticle

Proposed Theorems on the Lifts of Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection (NSNMC) in the Tangent Bundle

by Rajesh Kumar, Lalnunenga Colney and Mohammad Nazrul Islam Khan

Symmetry 2023, 15(11), 2037; https://doi.org/10.3390/sym15112037 - 9 Nov 2023

Cited by 5 | Viewed by 1550

Abstract

The main aim of the proposed paper is to investigate the lifts of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We investigate several properties of the lifts of the curvature tensor, the conformal curvature tensor, and the conharmonic curvature tensor of [...] Read more.

The main aim of the proposed paper is to investigate the lifts of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We investigate several properties of the lifts of the curvature tensor, the conformal curvature tensor, and the conharmonic curvature tensor of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We also study and discover that the lift of the Kenmotsu manifold that admit NSNMC is regular in the tangent bundle. Additionally, we find that the data provided by the lift of Ricci soliton on the lift of Ricci semi-symmetric Kenmotsu manifold that admits NSNMC in the tangent bundle are expanding. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry: Differential Geometry and Its Applications)

15 pages, 312 KiB

Open AccessArticle

Almost Ricci–Bourguignon Solitons on Doubly Warped Product Manifolds

by Sameh Shenawy, Nasser Bin Turki, Noha Syied and Carlo Mantica

Universe 2023, 9(9), 396; https://doi.org/10.3390/universe9090396 - 30 Aug 2023

Cited by 3 | Viewed by 1348

Abstract

This study aims at examining the effects of an almost Ricci–Bourguignon soliton structure on the base and fiber factor manifolds of a doubly warped product manifold. First, a number of preconditions and sufficiency criteria for an almost Ricci–Bourguignon soliton doubly warped product are [...] Read more.

This study aims at examining the effects of an almost Ricci–Bourguignon soliton structure on the base and fiber factor manifolds of a doubly warped product manifold. First, a number of preconditions and sufficiency criteria for an almost Ricci–Bourguignon soliton doubly warped product are addressed. Additionally, an almost Ricci–Bourguignon soliton on doubly warped product manifolds admitting a conformal vector field is taken into consideration. Finally, how the almost Ricci–Bourguignon soliton behaves in doubly warped product space–times is examined. Full article

(This article belongs to the Section Mathematical Physics)

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