| publication name | Generalized beta-conformal change of Finsler metrics. ArXiv Number: 0906.5369 [math.DG]. |
|---|---|
| Authors | Nabil L. Youssef, S. H. Abed and S. G. Elgendi, |
| year | 2010 |
| keywords | Generalized $beta$-conformal change, $beta$-conformal change, $beta$- change, conformal change, Randers change, Berwald space, Landesberg space, Locally Minkowskian space. |
| journal | Int. J. Geom. Meth. Mod. Phys. |
| volume | 7 (4) |
| issue | Not Available |
| pages | 565–582 |
| publisher | Not Available |
| Local/International | International |
| Paper Link | http://www.worldscientific.com/doi/abs/10.1142/S0219887810004440?journalCode=ijgmmp |
| Full paper | download |
| Supplementary materials | Not Available |
Abstract
In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $beta$-conformal change: $$L(x,y) longrightarrowoverline{L}(x,y) = f(e^{sigma(x)}L(x,y),beta(x,y)).$$ This transformation combines both $beta$-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated geometric objects, are obtained. Some invariants and various special Finsler spaces are investigated under this change. The most important changes of Finsler metrics existing in the literature are deduced from the generalized $beta$-conformal change as special cases.