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Hypersurfaces of a Riemannian manifold with semi-symmetric non-metric connection. (English) Zbl 0861.53056

A linear connection \(\nabla\) of torsion \(T\) on a Riemannian manifold \((M,g)\) is called semisymmetric nonmetric if there exists a 1-form \(\pi\) on \(M\) so that \[ \nabla_Xg=-\pi\otimes g(X,\cdot)-g(X,\cdot)\otimes \pi,\quad T=I\otimes \pi-\pi\otimes I. \] The authors establish the conditions under which a linear connection \(\overline{\nabla}\), induced by \(\nabla\) on an oriented hypersurface \(\overline{M}\subset M\), is also semisymmetric nonmetric. Other properties of the connection \(\overline{\nabla}\) are found, too.
Reviewer: V.Cruceanu (Iaşi)

MSC:

53C40 Global submanifolds
53C20 Global Riemannian geometry, including pinching
53C05 Connections (general theory)
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