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Keywords:
semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat
semi-symmetric metric connection; Levi-Civita connection; mean curvature; Ricci tensor; conformally flat
Summary:
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.
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