Lightlike Hypersurfaces on Manifolds Endowed with a Conformal Structure of Lorentzian Signature

Document Type

Article

Publication Date

1-1-1999

Abstract

The authors study the geometry of lightlike hypersurfaces on manifolds (M, c) endowed with a pseudoconformal structure c = CO(n - 1, 1) of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. On a lightlike hypersurface, the authors consider the fibration of isotropic geodesics and investigate their singular points and singular submanifolds. They construct a conformally invariant normalization of a lightlike hypersurface intrinsically connected with its geometry and investigate affine connections induced by this normalization. The authors also consider special classes of lightlike hypersurfaces. In particular, they investigate lightlike hypersurfaces for which the elements of the constructed normalization are integrable.

Identifier

0002519041 (Scopus)

Publication Title

Acta Applicandae Mathematicae

External Full Text Location

https://doi.org/10.1023/A:1006244706787

ISSN

01678019

First Page

255

Last Page

285

Issue

3

Volume

57

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