On special almost geodesic mappings of type π1 of spaces with affine connection

Abstract

A diffeomorphism f: A n →(A¯n) of two affine spaces is called a special almost geodesic mapping if

(a) Every geodesic of An passes into an almost geodesic curve of (A¯n) .

(b) (Pij h,k)+(Pij a)(Pak h)=aij(δk h) , where (Pij h) is the difference of the two respective connection coefficients and aij is a symmetric tensor.

In this paper, the authors discuss some tensorial properties of special almost geodesic mappings.