关于欧氏椭球面中平行和全脐超曲面的研究

On the Parallel and Totally Umbilical Hypersurfaces of the Euclidean Ellipsoid

中文关键词:  全脐  平行超曲面  椭球面

英文关键词:totally umbilical  parallel hypersurface  ellipsoid

中文摘要:

      我们给出了欧氏椭球面$Q^{n+1}(c,d)$中平行超曲面的完全分类,并且证明了$Q^{n+1}(c,d)$中的超曲面是全脐的当且仅当它是平行的.

英文摘要:

      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.