On geometry of hypersurfaces of a pseudoconformal space of Lorentzian signature

✍ Scribed by M.A. Akivis; V.V. Goldberg

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 904 KB
• Volume: 26
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(97)00041-7

✦ Synopsis

There are three types of hypersurfaces in a pseudoconformal space C; 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 C; that are closely connected with lightlike hypersurfaces and their Darboux mapping are also considered.