Some applications of prolonged covariant differentiation in Weyl spaces

In this paper, using the prolonged derivative and prolonged covariant derivative of satellites we define the so-called generalized geodesic coordinates in an n-dimensional Weyl space W_n and obtain the Bianchi identities for W_n. We then give the definition of a Recurrent-Weyl space (W_nR) and study some properties of hypersurfaces of (W _nR). As is well-known, in some papers [1] dealing with physical problems, one usually chooses a fixed metric and develop a theory under this restriction. We hope that the method used in this work will enable one to remove this restriction.