On Z-Projective Change of Kropina Spaces

Abstract

In this paper, we consider the projective change sigma : F -> (F) over tilde of metrics of the Kropina space F-n and the Finsler space (F) over tilde (n), respectively. It is known that The Douglas and the Weyl Curvature tensors remain invariant under the projective change of the Finsler metrics. Moreover, h-curvature tensor in the Berwald connection is invariant under the a special projective change named as Z-projective change. M. Fukui and T. Yamada studied in the projective change between two Finsler spaces. Then, B.D. Kim and H.Y. Park proved that if a symmetric space remains to be symmetric one under the Z-projective change then the space is of zero curvature. In present paper, we first investigated in the quantities which are invariant under the Z-projective change between two Finsler spaces. Then, we obtained the necessary and sufficient conditions for a projective change sigma : F -> (F) over tilde between a Kropina space F-n (n > 2) and a Finsler space (F) over tilde (n) (n > 2) to be a Z-projective change.