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Zbl 0982.53016
Ali, S.; Nivas, R.
On submanifolds immersed in a manifold with quarter symmetric connection. (English)
[J] Riv. Mat. Univ. Parma (6) 3, 11-23 (2000). ISSN 0035-6298

Let $M^{n+1}$ be a $C^\infty$-manifoldd with a quarter symmetric metric connection $\dot\nabla$ in the sense of {\it R. S. Mishra} and {\it S. N. Pandey} [Tensor 34, 1-7 (1980; Zbl 0451.53017)]. It is proved that the connection $\nabla$ 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 $\dot\nabla$ if and only if it is totally umbilic with respert to $\nabla$. The Gauss, Weingarten and Codazzi equations are deduced.
[Ülo Lumiste (Tartu)]

MSC 2000:: *53B25 Local submanifolds
53B05 Linear and affine connections

Keywords: submanifold of codimension 2; quarter symmetric metric connection; hypersurface

Citations: Zbl 0451.53017

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