In this paper, we consider the projective change σ : F → F of metrics of the Kropina space F n and the Finsler space F 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 σ : F → F between a Kropina space F n (n > 2) and a Finsler space F n (n > 2) to be a Z−projective change.
In [1], the generalization of Laguerre's function of direction for a surface in ordinary space to a hypersurface of a Riemannian space is obtained. The Laguerre's function of direction for a hypersurface of a Weyl space has been derived in [2]. In this paper, the generalization of Laguerre's function of direction to a hypersurface of generalized Weyl space is made.
In this paper, we show that the first Bianchi identity is valid for a generalized Weyl space having a semi-symmetric E-connection and that the second Bianchi identity is satisfied for a recurrent generalized Weyl space provided that the recurrence vector ψ l and the Vranceanu vector Ω l are related by ψ l = 2 n − 1 Ω l .
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