Mathematics – Differential Geometry
Scientific paper
1998-06-16
J. Geom. Phys. 26 (1998), no. 1-2, 112-126
Mathematics
Differential Geometry
LaTeX, 21 pages
Scientific paper
10.1016/S0393-0440(97)00041-7
There are three types of hypersurfaces in a pseudoconformal space C^n_1 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^n_1 that are closely connected with lightlike hypersurfaces and their Darboux mapping are also considered.
Akivis Maks A.
Goldberg Vladislav V.
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