On Totally Umbilical Submanifolds in Some Riemannian Manifolds
Received:May 20, 1987  
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Xuan Manyou 南昌陆军学院 
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      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 .
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