Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection

Ahmet Yücesan and Nihat Ayyildiz

Address: Department of Mathematics, University of Süleyman Demirel 32260 Isparta, Turkey


Abstract: 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.

AMSclassification: Primary: 53B15; Secondary: 53B30, 53C05, 53C50.

Keywords: semi-symmetric metric connection, Levi-Civita connection, mean curvature, Ricci tensor, conformally flat