Special Projective Motions in a Finsler Spaces

Abstract

In this paper, we consider a projective motion in a Finsler space whose deviation tensor satisfies certain conditions. It is proved that a projective motion in a Finsler space, whose deviation tensor satisfies (£ £ ) 0 k i i y BkHj − Bk Hj = , is necessarily an affine motion. It is also established that a projective motion which is also a curvature collineation and under which the covariant derivative of the deviation tensor is Lie-symmetric, is either an affine motion or the space is flat. In a recurrent Finsler space, if a projective motion is
a curvature collineation and it leaves the recurrence vector invariant, then the projective motion is necessarily an affine motion.