GENERALIZED β-CONFORMAL CHANGE AND SPECIAL FINSLER SPACES

Abstract

This work is a continuation of the paper [Generalized beta-conformal change of Finsler metrics, Int. J. Geom. Meth. Mod. Phys. 7(4) (2010) 565–582]. In the present paper, we investigate the change of Finsler metrics [Formula: see text] which we refer to as a generalized β-conformal change. Under this change, we study some special Finsler spaces, namely, quasi-C-reducible, semi-C-reducible, C-reducible, C 2 -like, S 3 -like and S 4 -like Finsler spaces. We obtain some characterizations of the energy β-change, the Randers change and the Kropina change. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized β-conformal change, which we call the b-condition, and investigate the geometric consequences of such a condition. Finally, we give the conditions under which a generalized β-conformal change is projective and generalize some known results in the literature.