Darboux function in a hypersurface of a Riemannian manifold with semi-symmetric metric connection

Abstract

In 1970, Yano, [1], studied Riemannian manifolds which admit semisymmetric metric connections whose curvature tensors vanish (see also [2]). The properties of a Riemannian manifold admitting a semi-symmetric metric connection were studied by many authors ([1], [3]). In [3], an expression of the curvature tensor of a manifold was obtained under assumption that the manifold admits a semi-symmetric metric connection with vanishing curvature tensor and recurrent torsion tensor. In this paper, we study a Darboux function in hypersurface of a Riemannian manifold with semi-symmetric metric connection. The purpose of this paper is that the relations between the Darboux function with respect to the linear connection and the Darboux function with respect to the Levi-Civita connection of a Riemannian manifold are obtained. In this paper, some theorems about this function are proved.