Turkish Journal of Mathematics
DOI
10.3906/mat-0806-11
Abstract
Let M^n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N^{n+1}_1, S be the squared norm of the second fundamental form of M^n in N^{n+1}_1. 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 M^n is totally umbilical, or \sup S=D(n, P) and M^n has two distinct principal curvatures.
Keywords
Constant scalar curvature, space-like hypersurface, second fundamental form, locally symmetric Lorentz space.
First Page
105
Last Page
114
Recommended Citation
LIU, JIANCHENG and WEI, LIN
(2010)
"A gap theorem for complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz spaces,"
Turkish Journal of Mathematics: Vol. 34:
No.
1, Article 10.
https://doi.org/10.3906/mat-0806-11
Available at:
https://journals.tubitak.gov.tr/math/vol34/iss1/10
