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On submanifolds immersed in a manifold with quarter symmetric connection. (English) Zbl 0982.53016
Let M n+1 be a C -manifoldd with a quarter symmetric metric connection ˙ in the sense of R. S. Mishra and S. N. Pandey [Tensor 34, 1-7 (1980; Zbl 0451.53017)]. It is proved that the connection induced on a hypersurface M n (as well as on a submanifold M n-1 of codimension 2) of such an M n+1 is also quarter symmetric. The hypersurface M n (resp. the submanifold M n-1 ) will be totally umbilic with respect to ˙ if and only if it is totally umbilic with respert to . The Gauss, Weingarten and Codazzi equations are deduced.
MSC:
53B25Local submanifolds
53B05Linear and affine connections