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  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371330).
Author NameAffiliation
Yinshan ZHANG School of Mathematics and Statistics, Zhengzhou University, Henan 450001, P. R. China 
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      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.
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