De, U. C.; Kamilya, D. Hypersurfaces of a Riemannian manifold with semi-symmetric non-metric connection. (English) Zbl 0861.53056 J. Indian Inst. Sci. 75, No. 6, 707-710 (1995). 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) Cited in 11 Documents MSC: 53C40 Global submanifolds 53C20 Global Riemannian geometry, including pinching 53C05 Connections (general theory) Keywords:semisymmetric nonmetric connection; linear connection; Riemannian manifold PDFBibTeX XMLCite \textit{U. C. De} and \textit{D. Kamilya}, J. Indian Inst. Sci. 75, No. 6, 707--710 (1995; Zbl 0861.53056)