Chen Inequalities on Lightlike Hypersurface of a Lorentzian Manifold with Semi-Symmetric Metric Connection

Abstract

In this paper, we introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection. Using this curvatures, we establish some inequalities for lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection. Considering these inequalities, we obtain the relation between Ricci curvature and scalar curvature endowed with semi-symmetric metric connection.

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

“…Z. Nakao generalized Imai’s approach of hypersurfaces by studying submanifolds of a Riemannian manifold with semi-symmetric metric connection [ 30 ]. The geometric inequalities on submanifolds in various manifolds with semi-symmetric metric connection have been extensively proven (see, e.g., [ 31 , 32 , 33 , 34 , 35 , 36 , 37 ]). However, only a few results are dedicated to the ambient of statistical manifolds endowed with semi-symmetric metric connection.…”

Some Inequalities on Half Lightlike Submanifolds of a Lorentzian Manifold with Semi-Symmetric Metric Connection

“…Firstly Chen inequalities on lightlike geometry were worked by Gülbahar, Kılıç and Keleş in [26] and [27]. Then Poyraz, Doğan and Yaşar studied Chen inequalities on lightlike hypersurface of a Lorentzian manifold with semi-symmetric metric connection in [28]. Some inequalities for screen conformal half lightlike submanifolds were established by Gülbahar and Kılıç in [29].…”

“…Some inequalities for screen conformal half lightlike submanifolds were established by Gülbahar and Kılıç in [29]. Finally, Poyraz and Doğan introduced Chen-like inequalities for half lightlike submanifolds of a Lorentzian manifold endowed with semi-symmetric metric connection in [30].…”

Lightlike submanifolds of metallic semi-Riemannian manifolds

“…Recent studies have been updated in [11]. Many studies on lightlike submanifolds have been reported by many geometers (see [1,3,13,14,23] and the references therein). In this paper, we follow the approach given by Duggal and Bejancu in [10].…”