On Infinitesimal Projective Transformations of the Tangent Bendle With the Complete Lift of A Finsler Metric

Abstract

Let (M,g) be a Finsler manifold and TM0 its slit tangent bundle with the complete lift metric ~g.

In this paper we prove that every infinitesimal complete lift projective transformation on (TM0,~g), is an infinitesimal affine transformation. Moreover, if (M,g) is a Landsberg manifold, then there is a one-to-one correspondence between infinitesimal complete lift projective transformations on (TM0,~g) and infinitesimal affine transformations on (M,g).