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Complete spacelike hypersurfaces with constant mean curvature in the de Sitter space: a gap theorem

Complete spacelike hypersurfaces with constant mean curvature in the de Sitter space: a gap theorem

Let $M^n$ be a complete spacelike hypersurface with constant mean curvature $H$ in the de Sitter space $S_1^{n+1}$. We use the operator $\phi =A-HI$, where $A$ is the second fundamental form of $M$, and the roots $B_H^- \le B_H^+$ of a certain second order polynomial, to prove that either $\vert\phi\vert^2\equiv …