On geometry of hypersurfaces of a pseudoconformal space of lorentzian signature

Document Type

Article

Publication Date

1-1-1998

Abstract

There are three types of hypersurfaces in a pseudoconformal space Cn1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a proper conformal structure, and timelike hypersurfaces are endowed with a conformal structure of Lorentzian type. Geometry of these two types of hypersurfaces can be studied in a manner that is similar to that for hypersurfaces of a proper conformal space. Lightlike hypersurfaces are endowed with a degenerate conformal structure. This is the reason that their investigation has special features. It is proved that under the Darboux mapping such hypersurfaces are transferred into tangentially degenerate (n - 1)-dimensional submanifolds of rank n - 2 located on the Darboux hyperquadric. The isotropic congruences of the space Cn1 that are closely connected with lightlike hypersurfaces and their Darboux mapping are also considered.

Identifier

0032089382 (Scopus)

Publication Title

Journal of Geometry and Physics

External Full Text Location

https://doi.org/10.1016/S0393-0440(97)00041-7

ISSN

03930440

First Page

112

Last Page

126

Issue

1-2

Volume

26

This document is currently not available here.

Share

COinS