Geodesic
On the dimension of the group of projective transformations of closed randers and Riemannian manifolds
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We construct a counterexample to Theorem 2 of [Rafie-Rad M., Rezaei B., SIGMA 7 (2011), 085, 12 pages].
Keywords: Finsler metrics, Randers metrics
Mots-clés : projective transformations. 
@article{SIGMA_2012_8_a6,
     author = {Vladimir S. Matveev},
     title = {On the dimension of the group of projective transformations of closed randers and {Riemannian} manifolds},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a6/}
}
TY  - JOUR
AU  - Vladimir S. Matveev
TI  - On the dimension of the group of projective transformations of closed randers and Riemannian manifolds
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2012
VL  - 8
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a6/
LA  - en
ID  - SIGMA_2012_8_a6
ER  - 
%0 Journal Article
%A Vladimir S. Matveev
%T On the dimension of the group of projective transformations of closed randers and Riemannian manifolds
%J Symmetry, integrability and geometry: methods and applications
%D 2012
%V 8
%U http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a6/
%G en
%F SIGMA_2012_8_a6
Vladimir S. Matveev. On the dimension of the group of projective transformations of closed randers and Riemannian manifolds. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a6/

[1] Bao D., Robles C., Shen Z., “Zermelo navigation on Riemannian manifolds”, J. Differential Geom., 66 (2004), 377–435 ; arXiv: math.DG/0311233 | MR | Zbl

[2] Beltrami E., “Risoluzione del problema: riportare i punti di una superficie sopra un piano in modo che le linee geodetische vengano rappresentante da linee rette”, Ann. di Mat., 1:7 (1865), 185–204

[3] Chen X., Deng S., “A new proof of a theorem of H.C. Wang”, Balkan J. Geom. Appl., 16 (2011), 25–26 | MR | Zbl

[4] Matveev V.S., “Die Vermutung von Obata für Dimension 2”, Arch. Math. (Basel), 82 (2004), 273–281 | DOI | MR | Zbl

[5] Matveev V.S., “Geometric explanation of the Beltrami theorem”, Int. J. Geom. Methods Mod. Phys., 3 (2006), 623–629 | DOI | MR | Zbl

[6] Matveev V.S., On projective equivalence and pointwise projective relation of Randers metrics, arXiv: 1112.6143

[7] Matveev V.S., “Proof of the projective Lichnerowicz–Obata conjecture”, J. Differential Geom., 75 (2007), 459–502 ; arXiv: math.DG/0407337 | MR | Zbl

[8] Matveev V.S., Troyanov M., The Binet–Legendre metric in Finsler geometry, arXiv: 1104.1647

[9] Rafie-Rad M., Rezaei B., “On the projective algebra of Randers metrics of constant flag curvature”, SIGMA, 7 (2011), 085, 12 pp. ; arXiv: 1108.6127 | DOI

[10] Wang H.C., “On Finsler spaces with completely integrable equations of Killing”, J. London Math. Soc., 22 (1947), 5–9 | DOI | MR | Zbl