Abstract
We give a characterization of a totally umbilic submanifold $M^n$ with parallel mean curvature vector of a Riemannian manifold $\tilde{M}^{n+p}$, that is an extrinsic sphere $M^n$ of $\tilde{M}^{n+p}$, in terms of the extrinsic shape of circles on $M^n$ in the ambient manifold $\tilde{M}^{n+p}$. This characterization is an improvement of Nomizu and Yano's result ([2]).
Citation
Masanori Kôzaki. Sadahiro Maeda. "A characterization of extrinsic spheres in a Riemannian manifold." Tsukuba J. Math. 26 (2) 291 - 297, December 2002. https://doi.org/10.21099/tkbjm/1496164426
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