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16 pages, 286 KiB

Open AccessArticle

A Study of Generalized Symmetric Metric Connection on Nearly Kenmotsu Manifolds

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

Symmetry 2025, 17(3), 317; https://doi.org/10.3390/sym17030317 - 20 Feb 2025

Viewed by 376

The focus of this research is on investigating a new category of generalized symmetric metric connections within nearly Kenmotsu manifolds. The study delves into recognizing the generalized symmetric connections of type

(α, β)

, which represent broader versions of [...] Read more.

(α, β)

, which represent broader versions of the semi-symmetric metric connection

(α = 1, β = 0)

and the quarter-symmetric metric connection

(α = 0, β = 1)

. Full article

(This article belongs to the Section Mathematics)

14 pages, 309 KiB

Open AccessArticle

Certain Curvature Conditions on Kenmotsu Manifolds and ★-η-Ricci Solitons

by Halil İbrahim Yoldaş, Abdul Haseeb and Fatemah Mofarreh

Axioms 2023, 12(2), 140; https://doi.org/10.3390/axioms12020140 - 30 Jan 2023

Cited by 9 | Viewed by 2106

Abstract

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with

★

-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of

★

[...] Read more.

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with

★

-η-Ricci solitons. First we find some necessary conditions for such a manifold to be φ-Einstein. Then, we study the notion of

★

-η-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. Full article

(This article belongs to the Special Issue Differential Geometry and Its Application)

14 pages, 352 KiB

Open AccessArticle

Generalized Lorentzian Sasakian-Space-Forms with

M

-Projective Curvature Tensor

by D. G. Prakasha, M. R. Amruthalakshmi, Fatemah Mofarreh and Abdul Haseeb

Mathematics 2022, 10(16), 2869; https://doi.org/10.3390/math10162869 - 11 Aug 2022

Cited by 3 | Viewed by 1468

Abstract

In this note, the generalized Lorentzian Sasakian-space-form

M_{1}^{2 n + 1} (f_{1}, f_{2}, f_{3})

satisfying certain constraints on the

M

-projective curvature tensor

W^{*}

is considered. Here, we characterize the structure [...] Read more.

In this note, the generalized Lorentzian Sasakian-space-form

M_{1}^{2 n + 1} (f_{1}, f_{2}, f_{3})

satisfying certain constraints on the

M

-projective curvature tensor

W^{*}

is considered. Here, we characterize the structure

M_{1}^{2 n + 1} (f_{1}, f_{2}, f_{3})

when it is, respectively,

M

-projectively flat,

M

-projectively semisymmetric,

M

-projectively pseudosymmetric, and

φ - M

-projectively semisymmetric. Moreover,

M_{1}^{2 n + 1} (f_{1}, f_{2}, f_{3})

satisfies the conditions

W^{*} (ζ, V_{1}) \cdot S = 0

W^{*} (ζ, V_{1}) \cdot R = 0

and

W^{*} (ζ, V_{1}) \cdot W^{*} = 0

are also examined. Finally, illustrative examples are given for obtained results. Full article

(This article belongs to the Special Issue Analytic and Geometric Inequalities: Theory and Applications)

9 pages, 246 KiB

Open AccessArticle

Generalized Affine Connections Associated with the Space of Centered Planes

by Olga Belova

Mathematics 2021, 9(7), 782; https://doi.org/10.3390/math9070782 - 5 Apr 2021

Cited by 4 | Viewed by 2017

Abstract

Our purpose is to study a space

Π

of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space

Π

are set in the generalized fiberings. Fields of these affine connection [...] Read more.

Our purpose is to study a space

Π

of centered m-planes in n-projective space. Generalized fiberings (with semi-gluing) are investigated. Planar and normal affine connections associated with the space

Π

are set in the generalized fiberings. Fields of these affine connection objects define torsion and curvature tensors. The canonical cases of planar and normal generalized affine connections are considered. Full article

(This article belongs to the Special Issue Differential Geometry of Spaces with Special Structures)

13 pages, 257 KiB

Open AccessArticle

Generalized Quasi-Einstein Manifolds in Contact Geometry

by İnan Ünal

Mathematics 2020, 8(9), 1592; https://doi.org/10.3390/math8091592 - 16 Sep 2020

Cited by 4 | Viewed by 2856

Abstract

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related to

M

-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold

S^{2 n + 1} (1) \times S^{1}

. Full article

(This article belongs to the Special Issue Selected Papers from the ICMASE2020—International Conference on Mathematics and Its Applications in Science and Engineering)

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