Einstein half lightlike submanifolds of a Lorentzian space form with a semi-symmetric metric connection

2014 ◽  
Vol 37 (4) ◽  
pp. 485-505
Author(s):  
D.H. Jin ◽  
J.W. Lee
Keyword(s):  
Space Form ◽  
Lorentzian Space ◽  
Metric Connection ◽  
Lightlike Submanifolds

scholarly journals Screen transversal cauchy Riemann lightlike submanifolds

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1581-1599
Author(s):  
Burçin Doḡan ◽  
Bayram Şahin ◽  
Erol Yaşar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
New Class ◽  
Metric Connection ◽  
Cauchy Riemann ◽  
Lightlike Submanifolds ◽  
Totally Real ◽  
Lightlike Submanifold

We introduce a new class of lightlike submanifolds, namely, Screen Transversal Cauchy Riemann (STCR)-lightlike submanifolds, of indefinite K?hler manifolds. We show that this new class is an umbrella of screen transversal lightlike, screen transversal totally real lightlike and CR-lightlike submanifolds. We give a few examples of a STCR lightlike submanifold, investigate the integrability of various distributions, obtain a characterization of such lightlike submanifolds in a complex space form and find new conditions for the induced connection to be a metric connection. Moreover, we investigate the existence of totally umbilical (STCR)-lightlike submanifolds and minimal (STCR)-lightlike submanifolds. The paper also contains several examples.

Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold

2021 ◽  
pp. 2150125
Author(s):  
Amrinder Pal Singh ◽  
Cyriaque Atindogbe ◽  
Rakesh Kumar ◽  
Varun Jain
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Lorentzian Manifold ◽  
Null Hypersurface ◽  
Lorentzian Space ◽  
Null Hypersurfaces

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

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