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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

Cited by 2 | Viewed by 782

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)

16 pages, 266 KB

Open AccessArticle

Geometry of LP-Sasakian Manifolds Admitting a General Connection

by Rajesh Kumar, Laltluangkima Chawngthu, Oğuzhan Bahadır and Meraj Ali Khan

Mathematics 2025, 13(6), 902; https://doi.org/10.3390/math13060902 - 7 Mar 2025

Viewed by 966

Abstract

This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context [...] Read more.

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

12 pages, 271 KB

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 1232

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 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)

15 pages, 300 KB

Open AccessArticle

Tangent Bundles Endowed with Quarter-Symmetric Non-Metric Connection (QSNMC) in a Lorentzian Para-Sasakian Manifold

by Rajesh Kumar, Lalnunenga Colney, Samesh Shenawy and Nasser Bin Turki

Mathematics 2023, 11(19), 4163; https://doi.org/10.3390/math11194163 - 4 Oct 2023

Cited by 7 | Viewed by 1526

Abstract

The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in an LP-Sasakian manifold to its tangent bundle are investigated. Necessary and sufficient conditions for the lifts of the Ricci tensor to be symmetric and skew-symmetric and the lifts of the projective Ricci tensor to be skew-symmetric in the tangent bundle are given. An example of complete lifts of four-dimensional LP-Sasakian manifolds in the tangent bundle is shown. Full article

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

13 pages, 291 KB

Open AccessArticle

Certain Results on the Lifts from an LP-Sasakian Manifold to Its Tangent Bundle Associated with a Quarter-Symmetric Metric Connection

by Mohammad Nazrul Islam Khan, Fatemah Mofarreh, Abdul Haseeb and Mohit Saxena

Symmetry 2023, 15(8), 1553; https://doi.org/10.3390/sym15081553 - 8 Aug 2023

Cited by 17 | Viewed by 1801

Abstract

The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly,

{(L P S)}_{n}

) to its tangent bundle

T M

associated with a Riemannian connection

D^{C}

[...] Read more.

The purpose of this study is to examine the complete lifts from the symmetric and concircular symmetric n-dimensional Lorentzian para-Sasakian manifolds (briefly,

{(L P S)}_{n}

) to its tangent bundle

T M

associated with a Riemannian connection

D^{C}

and a quarter-symmetric metric connection (QSMC)

{\bar{D}}^{C}

. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 2nd Edition)

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