scholarly journals LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

2015 ◽  
Vol 31 (1) ◽  
pp. 33-40
Author(s):  
Jong Moon Shin
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection ◽  
Lightlike Submanifolds

scholarly journals Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 79
Author(s):  
Tong Wu ◽  
Yong Wang
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection

In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codazzi, and Ricci equations in both cases. Moreover, Chen’s inequalities are also obtained in both cases. Some new examples based on non-integrable distributions in a Riemannian manifold with generalized semi-symmetric non-metric connections are proposed.

scholarly journals On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection

Symmetry ◽  
2017 ◽  
Vol 9 (7) ◽  
pp. 112 ◽  
Author(s):  
Jing Li ◽  
Guoqing He ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection

scholarly journals Screen conformal half-lightlike submanifolds

2004 ◽  
Vol 2004 (68) ◽  
pp. 3737-3753 ◽  
Author(s):  
K. L. Duggal ◽  
B. Sahin
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Ricci Tensor ◽  
Shape Operator ◽  
Close Relation ◽  
Screen Distribution ◽  
Lightlike Submanifolds ◽  
Half Lightlike Submanifold ◽  
Lightlike Submanifold

We study some properties of a half-lightlike submanifoldM, of a semi-Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. We show that any screen distributionS(TM)ofMis integrable and the geometry ofMhas a close relation with the nondegenerate geometry of a leaf ofS(TM). We prove some results on symmetric induced Ricci tensor and null sectional curvature of this class.

scholarly journals Lightlike submanifolds of metallic semi-Riemannian manifolds

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1781-1794
Author(s):  
Perktaş Yüksel ◽  
Feyza Erdoğan ◽  
Bilal Acet
Keyword(s):  
Riemannian Manifolds ◽  
Integrability Conditions ◽  
Metric Connection ◽  
Lightlike Submanifolds ◽  
Lightlike Hypersurfaces

Our aim in this paper is to investigate some special types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant lightlike submanifolds and screen semi-invariant lightlike hypersurfaces of metallic semi-Riemannian manifolds and give examples. We obtain some conditions for the induced connection to be a metric connection and present integrability conditions for the distributions involved in the definitions of such types.

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