Abstract:
In this paper, we investigate the nonnegative sectional curvature hypersurfaces in a real space form $M^{n+1}(c)$. We obtain some rigidity results of nonnegative sectional curvature hypersurfaces $M^{n+1}(c)$ with constant mean curvature or with constant scalar curvature. In particular, we give a certain characterization of the Riemannian product $S^k(a)\times S^{n-k}(\sqrt{1-a^2})$, $1\le k\le n-1$, in $S^{n+1}(1)$ and the Riemannian product $H^k(\operatorname{tanh}^2r-1)\times S^{n-k}(\operatorname{coth}^2r-1)$, $1\le k\le n-1$, in $H^{n+1}(-1)$.
Keywords:hypersurface in Euclidean $n$-space, space form, mean curvature, scalar curvature, principal curvature, sectional curvature, umbilical sphere, Codazzi equation, Ricci identity.
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