Abstract
Lightlike geometry has its applications in general relativity, particularly in black hole theory. Indeed, it is known that lightlike hypersurfaces are examples of physical models of Killing horizons in general relativity (Galloway, 2007). In this paper, we introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold. We investigate new results on a class of generic lightlike submanifolds M of an indefinite cosymplectic manifold .
Highlights
We introduce the definition of generic lightlike submanifolds of an indefinite cosymplectic manifold
In the generalization from Riemannian to semi-Riemannian manifolds, the induced metric may be degenerate lightlike there is a natural existence of lightlike submanifolds and for which the local and global geometry is completely different than nondengerate case
Mathematical Problems in Engineering theory of degenerate lightlike submanifolds. They constructed a transversal vector bundle of lightlike submanifold and investigated various properties of these manifolds. The geometry of both lightlike hypersurfaces and half lightlike submanifolds of indefinite cosymplectic manifolds was studied by Jin 3, 4
Summary
In the generalization from Riemannian to semi-Riemannian manifolds, the induced metric may be degenerate lightlike there is a natural existence of lightlike submanifolds and for which the local and global geometry is completely different than nondengerate case. The primary difference between the lightlike submanifolds and non-degenerate submanifolds is that in the first case, the normal vector bundle intersects with the tangent bundle. Mathematical Problems in Engineering theory of degenerate lightlike submanifolds. They constructed a transversal vector bundle of lightlike submanifold and investigated various properties of these manifolds. The geometry of both lightlike hypersurfaces and half lightlike submanifolds of indefinite cosymplectic manifolds was studied by Jin 3, 4. The objective of this paper is to study generic r-lightlike submanifolds M of an indefinite cosymplectic manifold M subject to the conditions: 1 M is totally umbilical, or 2 S TM is totally umbilical in M.
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