On the concircular vector fields of spaces with affine connection

Abstract

In this paper we study concircular vector fields of spaces with affine connection. We found the fundamental equation of these fields for the minimal requirements on the differentiability of the connection. The maximal numbers of linearly independent fields (with constant coefficients) is equal to n+1 and is realized only on projective flat spaces. Further we found a criterion on the Weyl tensor of the projective curvature of spaces, in which exist exactly n-1 independent concircular vector fields.