×

Pseudo-parallel space-like submanifolds of pseudo-Riemannian space forms. (Chinese. English summary) Zbl 1240.53077

Summary: The main purpose of this paper is to study space-like submanifolds of pseudo-Riemannian space forms. A necessary and sufficient condition for space-like hypersurfaces to be pseudo-parallel ones is obtained. Using Jordan triple system, a sufficient condition for pseudo-parallel space-like submanifolds to be totally geodesic ones is also given.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
PDFBibTeX XMLCite