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) × S n-k(√1 − a 2), 1 ≤ k ≤ n − 1, in S n+1(1) and the Riemannian product H k(tanh2 r − 1) × S n-k(coth2 r − 1), 1 ≤ k ≤ n − 1, in H n+1(−1).
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Published in Russian in Matematicheskie Zametki, 2009, Vol. 86, No. 5, pp. 776–793.
The text was submitted by the authors in English.
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Shu, S., Han, A.Y. Nonnegative sectional curvature hypersurfaces in a real space form. Math Notes 86, 729–743 (2009). https://doi.org/10.1134/S0001434609110157
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DOI: https://doi.org/10.1134/S0001434609110157