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Search Results (5)

Search Parameters:
Keywords = quarter-symmetric non-metric connection

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14 pages, 241 KiB  
Article
Analysis of Screen Generic Lightlike Submanifolds in an Indefinite Kaehler Statistical Manifold Endowed with a Quarter-Symmetric Non-Metric Connection
by Vandana Gupta, Jasleen Kaur, Oğuzhan Bahadır and Meraj Ali Khan
Axioms 2025, 14(3), 200; https://doi.org/10.3390/axioms14030200 - 8 Mar 2025
Viewed by 613
Abstract
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. [...] Read more.
This paper introduces the notion of screen generic lightlike submanifolds (SGLSs) of an indefinite Kaehler statistical manifold equipped with a quarter-symmetric non-metric (QSNM) connection, supported by suitable illustrations. Assertions for induced connection on the lightlike submanifold and integrability of the distributions are proved. The characterization theorems on parallelism and geodesicity of the SGLSs are presented. Results for the totally umbilic screen generic lightlike submanifold with a QSNM connection are also established. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application, 3rd Edition)
15 pages, 258 KiB  
Article
Quarter-Symmetric Non-Metric Connection of Non-Integrable Distributions
by Shuo Chen and Haiming Liu
Symmetry 2024, 16(7), 848; https://doi.org/10.3390/sym16070848 - 5 Jul 2024
Viewed by 1162
Abstract
In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then, the Gauss, Codazzi and [...] Read more.
In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then, the Gauss, Codazzi and Ricci equations are proved for non-integrable distributions with respect to a quarter-symmetric non-metric connection in generalized Riemannian manifold. Furthermore, we deduce Chen’s inequalities for non-integrable distributions of real space forms with a quarter-symmetric non-metric connection in generalized Riemannian manifold as applications. After that, we give some examples of non-integrable distributions in Riemannian manifold with quarter-symmetric non-metric connection. Full article
(This article belongs to the Section Mathematics)
11 pages, 281 KiB  
Article
Solitonical Inequality on Submanifolds in Trans-Sasakian Manifolds Coupled with a Slant Factor
by Mohd Danish Siddiqi and Rawan Bossly
Axioms 2024, 13(6), 370; https://doi.org/10.3390/axioms13060370 - 30 May 2024
Viewed by 701
Abstract
In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient [...] Read more.
In this article, we study the Ricci soliton on slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Moreover, we derive a lower-bound-type inequality for the slant submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection in terms of gradient Ricci solitons. We also characterize anti-invariant, invariant, quasi-umbilical submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection for which the same inequality case holds. Finally, we deduce the above inequalities in terms of a scalar concircular field on submanifolds of trans-Sasakian manifolds with a quarter symmetric non-metric connection. Full article
(This article belongs to the Special Issue Advances in Differential Geometry and Singularity Theory)
15 pages, 300 KiB  
Article
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 6 | Viewed by 1279
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 [...] Read more.
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)
15 pages, 317 KiB  
Article
E-Connections on the ε-Anti-Kähler Manifolds
by Zhizhi Chen, Yanlin Li, Aydin Gezer, Erkan Karakas and Cagri Karaman
Symmetry 2022, 14(9), 1899; https://doi.org/10.3390/sym14091899 - 11 Sep 2022
Viewed by 1570
Abstract
The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an ε-anti-Kähler manifold. Firstly, we deduce the relation between the Riemannian connection and the special forms of the quarter symmetric metric and non-metric connections. Then, we present [...] Read more.
The paper undertakes certain special forms of the quarter symmetric metric and non-metric connections on an ε-anti-Kähler manifold. Firstly, we deduce the relation between the Riemannian connection and the special forms of the quarter symmetric metric and non-metric connections. Then, we present some results concerning the torsion tensors of these connections. In addition, we find the forms of the curvature tensor, the Ricci curvature tensor and scalar curvature of such connections and we search the conditions for the ε-anti-Kähler manifold to be an Einstein space with respect to these connections. Finally, we study U(Ric)-vector fields with respect to these connections and give some results related to them. Full article
(This article belongs to the Section Mathematics)
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