THE SPACES OF FRENE

Abstract

It is well known that torsion-free spaces occupy a significant place in the field of research on the geometry of affinely connected spaces. This paper examines the properties of so-called Frenet spaces, which are spaces with affine connections and torsion. The concept of volume, which is preserved under parallel translations of vectors, is introduced in these spaces. Necessary and sufficient conditions are found for a torsion-free connection onto which a Frenet connection is mapped, preserving pseudoconnection, to be equiaffine. It is proved that for a mapping of two Frenet spaces onto each other to be geodesic, it is necessary and sufficient that the mean connections of these spaces coincide.