Kavli Affiliate: Yi Zhou
| First 5 Authors: Jianquan Ge, Ya Tao, Yi Zhou, ,
| Summary:
For compact submanifolds in Euclidean and Spherical space forms with Ricci
curvature bounded below by a function $alpha(n,k,H,c)$ of mean curvature, we
prove that the submanifold is either isometric to the Einstein Clifford torus,
or a topological sphere for the maximal bound $alpha(n,[frac{n}{2}],H,c)$, or
has up to $k$-th homology groups vanishing. This gives an almost complete
(except for the differentiable sphere theorem) characterization of compact
submanifolds with pinched Ricci curvature, generalizing celebrated rigidity
results obtained by Ejiri, Xu-Tian, Xu-Gu, Xu-Leng-Gu, Vlachos,
Dajczer-Vlachos.
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