Scalar curvature and symmetry properties of lightlike submanifolds (original) (raw)

On the sectional curvature of lightlike submanifolds

Journal of Inequalities and Applications, 2016

The main purpose of this paper is to show how to obtain rigidity theorems with the help of curvature invariants in submanifolds of a semi-Riemannian manifold. For this purpose, the bounded sectional curvature is introduced and some special submanifolds of r-lightlike submanifolds of a semi-Riemannian manifold are investigated.

Ricci Soliton Lightlike Submanifolds with Co-Dimension 222

Fundamental journal of mathematics and applications, 2023

The necessary requirements for half-lightlike and coisotropic lightlike submanifolds to be a Ricci soliton are obtained. Some examples of Ricci soliton half-lightlike and Ricci soliton coisotropic lightlike submanifolds are given. The Ricci soliton equation is investigated on totally geodesic, totally umbilical, and irrotational lightlike submanifolds.

Lightlike submanifolds of semi-Riemannian manifolds

Acta Applicandae Mathematicae, 1995

The purpose of this paper is to initiate a study of the differential geometry of lightlike (degenerate) submanifolds of semi-Riemannian manifolds. We construct the transversal vector bundle for an arbitrary lightlike submanifold and obtain results on the geometric structures induced on it. (1991). 53C42, 53C50,

Lightlike submanifolds of semi-Riemannian manifolds and applications

The purpose of this paper is to initiate a study of the differential geometry of lightlike (degenerate) submanifolds of semi-Riemannian manifolds. We construct the transversal vector bundle for an arbitrary lightlike submanifold and obtain results on the geometric structures induced on it. (1991). 53C42, 53C50,

The RICCI curvature of submanifolds and its applications

The Quarterly Journal of Mathematics, 2004

Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds.

On Lightlike Hypersurfaces of a Semi-Riemannian Space form

DergiPark (Istanbul University), 2003

In this paper, we study a Lightlike hypersurface of a semi-Riemann manifold. We show that a lightlike hypersurface is totally geodesic if and only if it is locally symmetric. Also, we show that a lightlike Hypersurface of IR 4m 4q (m, q > 1) is totally geodesic under some restrictions. Finally, we give some results on Ricci curvature of a lightlike hypersurface to be symmetric.

On scalar curvature in lightlike geometry

Journal of Geometry and Physics, 2007

We introduce the concept of induced scalar curvature of a class C[M ] of lightlike hypersurfaces (M, g, S(T M )), of a Lorentzian manifold, such that M admits a canonical screen distribution S(T M ), a canonical lightlike transversal vector bundle and an induced symmetric Ricci tensor. We prove that there exists such a class C[M ] of a globally hyperbolic warped product spacetime [3] of general relativity. In particular, we calculate scalar curvature of a member of C[M ] in a globally hyperbolic spacetime of constant curvature, supported by an example. MSC: 53C20; 53C50; 53B50 Subj. Class: Differential Geometry; General relativity

Riemannian geometry of half lightlike manifolds

We study a class of lightlike manifolds M , called half lightlike submanifold of codimension 2 of a Minkowski spacetime R n+2 1 . We show that some specified aspects of the null geometry of M reduce to the corresponding Riemannian geometry of its spacelike hypersurface.

Totally umbilical lightlike submanifolds

Kodai Mathematical Journal, 2003

This paper provides new results on a class of totally umbilical lightlike submanifolds in semi -Riemannian manifolds of constant curvature. We prove that the induced Ricci tensor of any such submanifold is symmetric if and only if its screen distribution is integrable. . 53B25, 53C40, 53C50. Key words: Degenerate metric, totally umbilical submanifolds.