On geodesic mappings of special Finsler spaces

@inProceedings{Bácsó1999,
abstract = {The author previously studied with F. Ilosvay and B. Kis [Publ. Math. 42, 139-144 (1993; Zbl 0796.53022)] the diffeomorphisms between two Finsler spaces $F^n= (M^n, L)$ and $\overline\{F\}^n= (M^n,\overline\{L\})$ which map the geodesics of $F^n$ to geodesics of $\overline\{F\}^n$ (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space $F^n$ and a Riemannian space $\overline\{\mathbb \{R\}\}^n$. The main result of this paper is as follows: if $F^n$ is of constant curvature $K$ and the mapping $F^n\rightarrow \overline\{\mathbb \{R\}\}^n$ is a strongly geodesic mapping then $K= 0$ or $K\ne 0$ and $\overline\{L\}= e^\{\varphi (x)\}L$.},
author = {Bácsó, Sándor},
booktitle = {Proceedings of the 18th Winter School "Geometry and Physics"},
keywords = {Winter school; Proceedings; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {83-87},
publisher = {Circolo Matematico di Palermo},
title = {On geodesic mappings of special Finsler spaces},
url = {http://eudml.org/doc/220895},
year = {1999},
}

TY - CLSWK
AU - Bácsó, Sándor
TI - On geodesic mappings of special Finsler spaces
T2 - Proceedings of the 18th Winter School "Geometry and Physics"
PY - 1999
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 83
EP - 87
AB - The author previously studied with F. Ilosvay and B. Kis [Publ. Math. 42, 139-144 (1993; Zbl 0796.53022)] the diffeomorphisms between two Finsler spaces $F^n= (M^n, L)$ and $\overline{F}^n= (M^n,\overline{L})$ which map the geodesics of $F^n$ to geodesics of $\overline{F}^n$ (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space $F^n$ and a Riemannian space $\overline{\mathbb {R}}^n$. The main result of this paper is as follows: if $F^n$ is of constant curvature $K$ and the mapping $F^n\rightarrow \overline{\mathbb {R}}^n$ is a strongly geodesic mapping then $K= 0$ or $K\ne 0$ and $\overline{L}= e^{\varphi (x)}L$.
KW - Winter school; Proceedings; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220895
ER -