Abstract: Using the equations of Gauss and Weingarten with respect to the LeviCivita connection, we gave the equations of Gauss and Weingarten for a nondegenerate hypersurface of a semiRiemannian manifold with a quartersymmetric metric connection, and obtained the Gauss curvature equation and CodazziMainardi equation for this kind of hypersurface. We could further study the properties of more general connection by using this result.

Key words: semiRiemannian manifold, nondegenerate hypersurface, quartersymmetric metric connection, LeviCivita connection