吴少华.常曲率空间关于直交全脐超曲面系的特征性质[J].数学研究及应用,1987,7(3):373~378
常曲率空间关于直交全脐超曲面系的特征性质
The Characterizations of the orthogonal System of Totally Umbilical Hypersurfaces in a Space of Constant Curvature
投稿时间:1984-02-25  
DOI:10.3770/j.issn:1000-341X.1987.03.003
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吴少华 杭州大学 
摘要点击次数: 1987
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英文摘要:
      Let Vn be Riemannian space of genernal constant curvature.In this paper, we have proved following;Theorem I If a Vn(n≥5 ) admits three mutually orthogonal families oftotally numbilical hypersurfaces such that they are of constant curvature and Einsteinian and of general constant curvature respectively, then Vn is space with constant curvature.Theorem 2 If a Vn ( n ≥ 5 ) admits three mutually orthogonal famities of totally umbilical hypersurfaces, of which one is conformally flat and other two are Einsteinian and of constant curvature respectively, and latter either is of constant meam curvature, then Vn is of constant curvature.
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