Lightlike submanifolds of semi-Riemannian manifolds
type: Item
instance of: scholarly article
title: Lightlike submanifolds of semi-Riemannian manifolds
zbMATH Open document ID: 0831.53040
DOI: 10.1007/BF00992847
author: Krishan Lal Duggal
author: Aurel Bejancu
published in: Acta Applicandae Mathematicae
publication date: 1995-10-09T00:00:00Z
review text: This paper initiates a general study of arbitrary lightlike (degenerate) submanifolds of semi-Riemannian manifolds. The authors construct the canonical lightlike transversal vector bundle of a lightlike submanifold with respect to a given screen distribution on it. Four cases are studied with respect to the degree of nullity of the lightlike submanifold and examples are given. The induced geometric structure on lightlike submanifolds is studied and the authors show that the leaves of the vertical vector bundle are totally geodesically immersed as lightlike submanifolds of the tangent bundle with a semi-Riemannian metric, and that lightlike immersions are affine immersions in the sense of Nomizu and Pinkall.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 790359
zbMATH Keywords: degenerate metric
zbMATH Keywords: second fundamental form
zbMATH Keywords: totally geodesic immersions
zbMATH Keywords: lightlike submanifold
Wikidata QID: Q115394639
reviewed by: Bernard Rouxel
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00992847
OpenAlex ID: W4240701137
description: scientific article; zbMATH DE number 790359