Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 1
A gap theorem for complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz spaces
- Pages
- 105–114
- DOI
- —
Abstract
Let Mn be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space Nn+11, S be the squared norm of the second fundamental form of Mn in Nn+11. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and Mn is totally umbilical, or \sup S=D(n, P) and Mn has two distinct principal curvatures.
Özet
Let Mn be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space Nn+11, S be the squared norm of the second fundamental form of Mn in Nn+11. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and Mn is totally umbilical, or \sup S=D(n, P) and Mn has two distinct principal curvatures.