Geodesic
Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 77-88

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We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection. Eventually, we establish conformal equations of Gauss curvature and Codazzi-Mainardi.
Classification : 53B15, 53B30, 53C05, 53C50
Keywords: semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat 
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     title = {Non-degenerate hypersurfaces {of~a~semi-Riemannian} manifold with~a~semi-symmetric metric connection},
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Yücesan, Ahmet; Ayyildiz, Nihat. Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/ARM_2008__44_1_a8/