In this paper, we investigate the change
of Finslr metrics $$L(x,y) longrightarrowoverline{L}(x,y) =
f(e^{sigma(x)}L(x,y),beta(x,y)),$$ which we refer to as a
generalized $beta$-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
$beta$-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 $beta$-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
$beta$-conformal change is projective and generalize some known
results in the literature. |
