On Equitorsion Concircular Tensors of Generalized Riemannian Spaces

Abstract

In this paper we consider concircular vector fields of  manifolds with  non-symmetric metric tensor.  The subject of our paper is an  equitorsion concircular mapping. A mapping $f:\mathbb{GR}_N \rightarrow \mathbb{G\overline R}_N$ is an {equitorsion} if the torsion tensors of the spaces $\mathbb{GR}_N$ and $\mathbb{G\overline R}_N$ are equal.

For an equitorsion concircular  mapping of two generalized Riemannian spaces $\mathbb{GR}_N$ and $\mathbb{G\overline{R}}_N$, we obtain some invariant curvature tensors of this mapping $\underset\theta Z,\;\theta=1,2,\ldots,5,$ given by equations (3.14, 3.21, 3.28, 3.31, 3.38). These quantities are generalizations of the concircular tensor $Z$ given by equation (2.5).