On geodesic mappings of special Finsler spaces

Proceedings of the 18th Winter School "Geometry and Physics", GDML_Books, (1999), p. 83-87 / Harvested from

Résumé

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 ${\bar{F}}^{n} = (M^{n}, \bar{L})$ which map the geodesics of $F^{n}$ to geodesics of ${\bar{F}}^{n}$ (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space $F^{n}$ and a Riemannian space ${\bar{ℝ}}^{n}$ . The main result of this paper is as follows: if $F^{n}$ is of constant curvature $K$ and the mapping $F^{n} \to {\bar{ℝ}}^{n}$ is a strongly geodesic mapping then $K = 0$ or $K \neq 0$ and $\bar{L} = e^{ϕ (x)} L$ .

MR MR1692259 | Zbl 0976.53079

EUDML-ID : urn:eudml:doc:220895
Mots clés:

@article{701627,
     title = {On geodesic mappings of special Finsler spaces},
     booktitle = {Proceedings of the 18th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1999},
     pages = {83-87},
     mrnumber = {MR1692259},
     zbl = {0976.53079},
     url = {http://dml.mathdoc.fr/item/701627}
}

Bácsó, Sándor. On geodesic mappings of special Finsler spaces, dans Proceedings of the 18th Winter School "Geometry and Physics", GDML_Books,  (1999), pp. 83-87. http://gdmltest.u-ga.fr/item/701627/