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A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei

Turkish Journal of Mathematics

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.