Conditions on a null hypersurface of a Lorentzian manifold to be a null cone

2019 ◽  
Vol 145 ◽  
pp. 103469
Author(s):  
Manuel Gutiérrez ◽  
Benjamín Olea
Keyword(s):  
Lorentzian Manifold ◽  
Null Hypersurface ◽  
Null Cone

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.

scholarly journals Concurrent Vector Fields on Lightlike Hypersurfaces

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 59
Author(s):  
Erol Kılıç ◽  
Mehmet Gülbahar ◽  
Ecem Kavuk
Keyword(s):  
Vector Fields ◽  
Ricci Soliton ◽  
Lorentzian Manifold ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Lightlike Hypersurfaces

Concurrent vector fields lying on lightlike hypersurfaces of a Lorentzian manifold are investigated. Obtained results dealing with concurrent vector fields are discussed for totally umbilical lightlike hypersurfaces and totally geodesic lightlike hypersurfaces. Furthermore, Ricci soliton lightlike hypersurfaces admitting concurrent vector fields are studied and some characterizations for this frame of hypersurfaces are obtained.

scholarly journals On Co-screen Conformality of 1-lightlike Submanifolds in a Lorentzian Manifold

2015 ◽  
Vol 7 (2) ◽  
pp. 76
Author(s):  
Erol Kilic ◽  
Sadik Keles ◽  
Mehmet Gulbahar
Keyword(s):  
Ricci Tensor ◽  
Lorentzian Manifold ◽  
Conformal Killing ◽  
Screen Distribution ◽  
Locally Conformal ◽  
Lightlike Submanifolds

In this paper, the co-screen conformal 1-lightlike submanifolds of a Lorentzian manifoldare introduced as a generalization of co-screen locally half-lightlike submanifolds in(Wang,  Wang {\&} Liu, 2013; Wang {\&} Liu, 2013) and two examples are given whichone is co-screen locally conformal andthe other is not. Some results are obtained on these submanifolds whichthe co-screen distribution is conformal Killing on the ambient manifold.The induced Ricci tensor of  co-screen conformal 1-lightlike submanifolds isinvestigated.

scholarly journals On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes

1993 ◽  
Vol 55 (1) ◽  
pp. 41-59 ◽  
Author(s):  
Klaus Ecker
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
A Priori Estimates ◽  
A Priori ◽  
Curvature Flow ◽  
Lorentzian Manifold ◽  
Asymptotically Flat ◽  
Spacelike Hypersurfaces ◽  
Flat Spacetimes ◽  
Weaker Conditions

AbstractWe prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.

Multi-Centered Metric In 4-Dimensional Lorentzian Manifold

2010 ◽  
Author(s):  
Seramika A. Wahyoedi ◽  
Fiki T. Akbar ◽  
Bobby E. Gunara ◽  
Khairurrijal ◽  
Mikrajuddin Abdullah ◽  
...  
Keyword(s):  
Lorentzian Manifold

Newtonian gravity on the null cone

1983 ◽  
Vol 24 (5) ◽  
pp. 1193-1198 ◽  
Author(s):  
J. Winicour
Keyword(s):  
Newtonian Gravity ◽  
Null Cone

Geodesics in Static Lorentzian Manifolds with Critical Quadratic Behavior

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Bartolo ◽  
A.M. Candela ◽  
J.L. Flores ◽  
M. Sánchez
Keyword(s):  
Lorentzian Manifold ◽  
Lorentzian Manifolds ◽  
Geodesic Connectedness

AbstractThe aim of this paper is t o study the geodesic connectedness of a complete static Lorentzian manifold (M.〈·, ·〉

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