S. P. Singh

ON PROJECTIVE MOTION IN FINSLER SPACES II

K. Takano [4] in a series of papers has studied and developed affine motion in non-Riemannian K*-spaces. R.S. Sinha [6] has studied affine motions in recurrent Finsler spaces. The existence of projective motion in a symmetric Finsler space was discussed by F.Meher [7]. Let ξi be a contravariant vector generating an infinitesimal mapping n: Fn → F¯ n of type x¯ i = xi + ξ i(x)dt. Such a mapping, when preserving the parallelism of a pair of any two vectors in Fn, defines an affine motion. The above infinitesimal transformation defines a projective motion if it transforms the system of geodesics into that of geodesics. The present authors [8] have discussed projective curvature collineation by considering vanishing of the Lie-derivature of the curvature tensor in Finsler space. The purpose of this paper is to study projective motion in Finsler spaces for the curvature tensor R*ijkh. The notations used in the sequel are due to E. Cartan [1] and H. Rund [3].

MOTION WITH CONTRA FIELD IN FINSLER SPACES

Abstract An affine motion of special type was developed in non-Riemannian K*-spaces by Takano [5]. He called such a motion an affine motion with contra field. The same concept was extended to Finsler spaces by Misra and Meher [1]. Later, the same authors [2] studied CA-motion in a projective symmetric Finsler space. An affine motion satisfying the condition υi (j) = ρδi j, where ρ(x, x) is a non-zero scalar function, is called affine motion with contra field or briefly CA-motion. Recently the present author [4] has discussed projective motion in Finsler space F n. The purpose of this paper is to study affine and projective motions with contra field in Finsler spaces. The notations of Rund [3] are used in the sequel.