| On the Parallel and Totally Umbilical Hypersurfaces of the Euclidean Ellipsoid |
| Received:November 05, 2015 Revised:March 09, 2016 |
| Key Words:
totally umbilical parallel hypersurface ellipsoid
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371330). |
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| Abstract: |
| We give a complete classification of parallel hypersurfaces in the Euclidean ellipsoid $Q^{n+1}(c,d)$. Moreover, we prove that a hypersurface in $Q^{n+1}(c,d)$ is totally umbilical, if and only if it is parallel. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.05.009 |
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