Energy <i>β</i>-Conformal Change and Special Finsler Spaces

Abstract

The main aim of the present paper is to establish an intrinsic investigation of the energy β -conformal change of the most important special Finsler spaces, namely, C h -recurrent, C v -recurrent, C 0 -recurrent, S v -recurrent, quasi-C-reducible, semi-C-reducible, C-reducible, P-reducible, C 2 -like, S 3 -like, P 2 -like and h-isotropic, ···, etc. Necessary and sufficient conditions for such special Finsler manifolds to be invariant under an energy β -conformal change are obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.