Generalized $β$-conformal change and special Finsler spaces

Details Generalized $β$-conformal change and special Finsler spaces Generalized $β$-conformal change and special Finsler spaces

2010-04-30

arxiv.org/abs/1004.5478v3

Mathematics

Differential Geometry

References added, some modifications are performed, LateX file, 24 pages

Scientific paper

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ 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 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 condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.

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