| On Totally Umbilical Submanifolds in Some Riemannian Manifolds |
| Received:May 20, 1987 |
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| Abstract: |
| The main result obtaind in this paper is that :Let M be a totally umbilical submanifolds in Riemannian manifold N. If the Weyl conformal curvature tensor for N satisfies the following condition: ▽xC=ω(X)C, for some 1-form ω and any vector field X in M, then M is con-formally flat or it is totally geodesic . |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1989.02.012 |
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