| The Characterizations of the orthogonal System of Totally Umbilical Hypersurfaces in a Space of Constant Curvature |
| Received:February 25, 1984 |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1987.03.003 |
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