Compact null hypersurfaces in Lorentzian manifolds

2021 ◽  
Vol 21 (2) ◽  
pp. 251-263
Author(s):  
C. Atindogbé ◽  
M. Gutiérrez ◽  
R. Hounnonkpe
Keyword(s):  
Global Symmetries ◽  
Lorentzian Manifold ◽  
Lorentzian Manifolds ◽  
Geometric Properties ◽  
Totally Geodesic ◽  
Null Hypersurfaces ◽  
Ambient Manifold ◽  
The Family

Abstract We show how the topological and geometric properties of the family of null hypersurfaces in a Lorentzian manifold are related with the properties of the ambient manifold itself. In particular, we focus in how the presence of global symmetries and curvature conditions restrict the existence of compact null hypersurfaces. We use these results to show the influence on the existence of compact totally umbilic null hypersurfaceswhich are not totally geodesic. Finally we describe the restrictions that they impose in causality theory.

Null hypersurfaces in Lorentzian manifolds II

1981 ◽  
Vol 89 (3) ◽  
pp. 525-532 ◽  
Author(s):  
K. Katsuno
Keyword(s):  
Lorentzian Manifold ◽  
Parameter Family ◽  
Lorentzian Manifolds ◽  
Geometrical Properties ◽  
Null Hypersurfaces

This paper is a continuation of (8), and is concerned with geometrical properties of special null hypersurfaces. In particular, on a one-parameter family of null hypersurfaces in four-dimensional Lorentzian manifoldV4, we consider the relation between their normal and the Debever vectors, especially repeated ones. Throughout this paper, the same notations as those in (8) are used.

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.

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.

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.

GEOMETRY OF BISECTORS FOR STRICTLY CONVEX DISTANCES

1996 ◽  
Vol 06 (01) ◽  
pp. 45-58 ◽  
Author(s):  
A.G. CORBALAN ◽  
M. MAZON ◽  
T. RECIO
Keyword(s):  
The Other ◽  
Geometric Properties ◽  
Asymptotic Line ◽  
Strictly Convex ◽  
Line Section ◽  
Other Hand ◽  
The Family

In this paper we study some unexpected geometric properties of the family of bisector lines for a convex distance d, showing that bisectors do not always have an asymptotic line (Section 2). Moreover, although bisectors are homeomorphic to lines, pairs of them can exist intersecting infinitely many times (Section 3). This leads to the conclusion that convex distances are not always nice in the sense of Klein and Wood.7 On the other hand, we prove that distances d, having d-balls whose boundary is given by finitely many algebraic conditions, produce nice distances (Section 3).

scholarly journals Null hypersurfaces in Lorentzian manifolds with the null energy condition

2020 ◽  
Vol 155 ◽  
pp. 103751
Author(s):  
Shintaro Akamine ◽  
Atsufumi Honda ◽  
Masaaki Umehara ◽  
Kotaro Yamada
Keyword(s):  
Energy Condition ◽  
Null Energy Condition ◽  
Lorentzian Manifolds ◽  
Null Hypersurfaces

Real Stable, Stable, And Not-So Stable Polyhedra: All Stemming From A New Family

1996 ◽  
Vol 11 (1-2) ◽  
pp. 251-256
Author(s):  
Joseph D. Clinton
Keyword(s):  
Surface Area ◽  
The Other ◽  
Geometric Properties ◽  
New Family ◽  
Regular Polyhedra ◽  
The Family ◽  
Out Of Plane ◽  
New Form ◽  
Axes Of Symmetry

A description of a Family of Polyhedra is given where the parent forms are the five regular polyhedra. The facial planes of the parent forms are subdivided into right triangles and by a series of rearrangements are allowed to move out of plane thus creating new volumetric forms while maintaining the same surface area. The axes of symmetry of the parent polyhedra are preserved. One new form is less stable than the parent and the other is more stable than the parent; thus giving rise to a family of real stable, stable and not-so stable polyhedra. Illustrations of all fifteen polyhedra in the family are given along with tables describing several of their geometric properties. The influence of precision on geometrical stability will also be demonstrated as related to architectural applications.

scholarly journals Certain results on invariant submanifolds of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$-space

2021 ◽  
Author(s):  
Mehmet Atc̣eken
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Curvature ◽  
Invariant Submanifold ◽  
Totally Geodesic ◽  
Ambient Manifold ◽  
Riemannian Curvature Tensor ◽  
Nullity Distribution ◽  
Invariant Submanifolds ◽  
Almost All ◽  
Necessary And Sufficient

AbstractIn the present paper, we study invariant submanifolds of almost Kenmotsu structures whose Riemannian curvature tensor has $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -nullity distribution. Since the geometry of an invariant submanifold inherits almost all properties of the ambient manifold, we research how the functions $$\kappa ,\mu $$ κ , μ and $$\nu $$ ν behave on the submanifold. In this connection, necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -space to be totally geodesic under some conditions.

Sign in / Sign up

Export Citation Format

Share Document