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Generalized beta-conformal change of Finsler metrics. ArXiv Number: 0906.5369 [math.DG].
Int. J. Geom. Meth. Mod. Phys. • 2010
Publication Information
Authors
Nabil L. Youssef, S. H. Abed and S. G. Elgendi,
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.
Publisher
Not Available
Volume
7 (4)
Issue
Not Available
Pages
565–582
publication.type
International
Paper Link
Open Link
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.
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.