Convex surfaces in Lorentzian spaces of constant curvature. (Surfaces convexes dans des espaces lorentziens à courbure constante.) (French) Zbl 0864.53016

Schlenker, Jean-Marc

Commun. Anal. Geom. 4, No. 2, 285-331 (1996).

In this paper are studied the convex surfaces in Lorentzian spaces of constant curvature; the isometric immersions of compact surfaces with curvature \(K< K_0\), in 3-dimensional Lorentz spaces (with constant curvature \(K_0)\); the existence and uniqueness for some isometric immersions of compact surfaces in de Sitter space. The results may be generalized to complete surfaces.

Reviewer: P.Stavre (Craiova)

MSC:

53B25	Local submanifolds
53B30	Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

convex surfaces; Lorentzian spaces of constant curvature; compact surfaces; isometric immersions