Half-Symmetric Connections of Generalized Riemannian Spaces

Abstract

In this article, we generalize Yano’s concept of a half-symmetric affine connection. With respect to this generalization, we obtain five linearly independent curvature tensors. In the following, we examine which special kinds of affine connections may be the generalized half-symmetric affine connection. At the end of this work, we generalize the term of Killing’s vector given by Yano to affine Killing, conformal Killing, projective Killing, harmonic, and covariant and contravariant analytic vectors.