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.

scholarly journals On some types of lightlike submanifolds of golden semi-Riemannian manifolds

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3231-3242
Author(s):  
Feyza Erdoğan
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Metric Connection ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterizations of screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. Finally, we give two examples.

scholarly journals Lightlike hypersurfaces of an (ε)-para Sasakian manifold with a semi-symmetric non-metric connection

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5767-5786
Author(s):  
Feyza Erdoğan ◽  
Selcen Perktaş
Keyword(s):  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Lightlike Hypersurface ◽  
Ambient Manifold ◽  
Integrability Conditions ◽  
Metric Connection ◽  
Lightlike Hypersurfaces

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an (?)-para Sasakian manifold endowed with a semi-symmetric non-metric connection. We obtain a condition for such a lightlike hypersurface to be totally geodesic. We define invariant and screen semi-invariant lightlike hypersurfaces of (?)-para Sasakian manifolds with a semi-symmetric non-metric connection. Also, we obtain integrability conditions for the distributions D ? ??? and D' ? ??? of a screen semi-invariant lightlike hypersurface of an (?)-para Sasakian manifolds with a semi-symmetric non-metric connection.

scholarly journals Lightlike hypersurfaces of metallic semi-Riemannian manifolds

2018 ◽  
Vol 15 (12) ◽  
pp. 1850201 ◽  
Author(s):  
Bilal Eftal Acet
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Geometric Properties ◽  
Lightlike Hypersurface ◽  
Integrability Conditions ◽  
Lightlike Hypersurfaces ◽  
Induced Structure

In our paper, we introduce and study lightlike hypersurfaces of a metallic semi-Riemannian manifold. We examine some geometric properties of invariant lightlike hypersurfaces. We show that the induced structure on an invariant lightlike hypersurface is also metallic. We also define screen semi-invariant lightlike hypersurfaces, investigate integrability conditions for the distributions and give some examples.

Lightlike submanifolds of semi-Riemannian manifolds

1995 ◽  
Vol 38 (2) ◽  
pp. 197-215 ◽  
Author(s):  
Aurel Bejancu ◽  
K. L. Duggal
Keyword(s):  
Riemannian Manifolds ◽  
Lightlike Submanifolds

scholarly journals Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter-Symmetric Nonmetric Connections

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Erol Kılıç ◽  
Oğuzhan Bahadır
Keyword(s):  
Riemannian Manifolds ◽  
Product Structure ◽  
Product Manifold ◽  
Riemannian Product ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Lightlike Hypersurfaces ◽  
Equivalent Conditions

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical anti-invariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quarter-symmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions for integrability of distributions with respect to the Levi-Civita connection of semi-Riemannian manifolds and the quarter-symmetric nonmetric connection, and we obtain some results.

scholarly journals Generic Lightlike Submanifolds of an Indefinite Cosymplectic Manifold

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Dae Ho Jin ◽  
Jae Won Lee
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Physical Models ◽  
Hole Theory ◽  
Cosymplectic Manifold ◽  
Definition Of ◽  
Lightlike Submanifolds ◽  
Lightlike Hypersurfaces ◽  
Killing Horizons

Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds of an indefinite cosymplectic manifold .

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