| You are in:Home/Publications/Metrizability of Holonomy Invariant Projective Deformation of Sprays | |
Dr. Salah Gomaa Ahmed Ali Elgendi :: Publications: |
|
| Title: | Metrizability of Holonomy Invariant Projective Deformation of Sprays
|
| Authors: | Salah Elgendi & Zoltan Muzsnay |
| Year: | 2020 |
| Keywords: | spray; projective deformation; metrizability problem; holonomy invariant function; holonomy distribution. |
| Journal: | Canadian Mathematical Bulletin |
| Volume: | Not Available |
| Issue: | Not Available |
| Pages: | 1-14 |
| Publisher: | Not Available |
| Local/International: | International |
| Paper Link: | |
| Full paper | Salah Gomaa Ahmed Ali Elgendi_Master.pdf |
| 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. |
