Staff Members - Benha University
Metrizability of Holonomy Invariant Projective Deformation of Sprays
Canadian Mathematical Bulletin • 2020
Publication Information
Authors
Salah Elgendi & Zoltan Muzsnay
Keywords
spray; projective deformation; metrizability problem; holonomy invariant function; holonomy distribution.
Journal
Canadian Mathematical Bulletin
Publisher
Not Available
Volume
Not Available
Issue
Not Available
Pages
1-14
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
In this paper, we consider projective deformation of the geodesic system of Finsler spaces by
holonomy invariant functions. Starting with a Finsler spray S and a holonomy invariant function P,
we investigate the metrizability property of the projective deformation ̃S = S − 2λPC. We prove that
for any holonomy invariant nontrivial function P and for almost every value λ ∈ R, such deformation
is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray.
In these cases, the holonomy invariant function P is necessarily one of the principal curvatures of the
geodesic structure.
holonomy invariant functions. Starting with a Finsler spray S and a holonomy invariant function P,
we investigate the metrizability property of the projective deformation ̃S = S − 2λPC. We prove that
for any holonomy invariant nontrivial function P and for almost every value λ ∈ R, such deformation
is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray.
In these cases, the holonomy invariant function P is necessarily one of the principal curvatures of the
geodesic structure.