Notes on product semisymmetric connection in a locally decomposable Riemannian space

Abstract

The purpose of this paper is to investigate the product semi-symmetric connection in a locally decomposable Riemannian space. The curvature tensors of this connection were considered. Some properties of almost product structure, some properties of torsion tensor of product semi-symmetric connection and some relations between curvature tensors and almost product structure are given. Also, the paper checks a special case of such connection when its generator is a gradient vector.