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

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.

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.〈·, ·〉

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.

$r$-Almost Newton-Ricci solitons immersed in a Lorentzian manifold: examples, nonexistence and rigidity

2020 ◽  
Vol 43 (1) ◽  
pp. 42-56
Author(s):  
Antonio W. Cunha ◽  
Eudes L. de Lima ◽  
Henrique F. de Lima
Keyword(s):  
Lorentzian Manifold ◽  
Ricci Solitons

scholarly journals RECOVERY OF ZEROTH ORDER COEFFICIENTS IN NON-LINEAR WAVE EQUATIONS

2020 ◽  
pp. 1-27
Author(s):  
Ali Feizmohammadi ◽  
Lauri Oksanen
Keyword(s):  
Wave Equations ◽  
Model Problem ◽  
Wave Interaction ◽  
Lorentzian Manifold ◽  
Gaussian Beams ◽  
Linear Wave ◽  
Lorentzian Manifolds ◽  
Solution Map ◽  
Globally Hyperbolic ◽  
Linear Wave Equations

This paper is concerned with the resolution of an inverse problem related to the recovery of a function $V$ from the source to solution map of the semi-linear equation $(\Box _{g}+V)u+u^{3}=0$ on a globally hyperbolic Lorentzian manifold $({\mathcal{M}},g)$ . We first study the simpler model problem, where $({\mathcal{M}},g)$ is the Minkowski space, and prove the unique recovery of $V$ through the use of geometric optics and a three-fold wave interaction arising from the cubic non-linearity. Subsequently, the result is generalized to globally hyperbolic Lorentzian manifolds by using Gaussian beams.

scholarly journals Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations

2017 ◽  
Vol 2019 (16) ◽  
pp. 5087-5126 ◽  
Author(s):  
Yavar Kian ◽  
Lauri Oksanen
Keyword(s):  
Riemannian Manifold ◽  
Hyperbolic Equations ◽  
Lorentzian Manifold ◽  
Cauchy Data ◽  
Time Dependent ◽  
Unique Determination ◽  
Data Set ◽  
Dependent Potential ◽  
Calderón Problem

Abstract Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we study the inverse boundary value problem of determining a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_g u+q(t,x)u=0$ in ${\overline M}=(0,T)\times M$ with $T>0$. Under suitable geometric assumptions we prove global unique determination of $q\in L^\infty({\overline M})$ given the Cauchy data set on the whole boundary $\partial {\overline M}$, or on certain subsets of $\partial {\overline M}$. Our problem can be seen as an analogue of the Calderón problem on the Lorentzian manifold $({\overline M}, dt^2 - g)$.

Hypersurfaces with Light-Like Points in a Lorentzian Manifold

2018 ◽  
Vol 29 (4) ◽  
pp. 3405-3437 ◽  
Author(s):  
M. Umehara ◽  
K. Yamada
Keyword(s):  
Lorentzian Manifold
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