| 
 SIGMA 8 (2012), 007, 4 pages      arXiv:1201.3575     
https://doi.org/10.3842/SIGMA.2012.007 
On the Dimension of the Group of Projective Transformations of Closed Randers  and Riemannian Manifolds
Vladimir S. Matveev
 Institute of Mathematics,  Friedrich-Schiller-Universität Jena,  07737 Jena, Germany
 
 
Received January 18, 2012, in final form February 21, 2012; Published online February 23, 2012 
Abstract
 
We construct a counterexample to Theorem 2 of [Rafie-Rad M., Rezaei B., SIGMA 7 (2011), 085, 12 pages].
  
 Key words:
Finsler metrics; Randers metrics; projective transformations. 
pdf (257 kb)  
tex (9 kb)
 
 
References
 
- Bao D., Robles C., Shen Z.,
Zermelo navigation on Riemannian manifolds,
J. Differential Geom. 66 (2004), 377-435,
math.DG/0311233.
 
- 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 (1865), no. 7, 185-204.
 
- Chen X., Deng S., A new proof of a theorem of H.C. Wang,
Balkan J. Geom. Appl. 16 (2011), 25-26.
 
- Matveev V.S.,
Die Vermutung von Obata für Dimension 2,
Arch. Math. (Basel) 82 (2004), 273-281.
 
- Matveev V.S.,
Geometric explanation of the Beltrami theorem,
Int. J. Geom. Methods Mod. Phys. 3 (2006), 623-629.
 
- Matveev V.S.,
On projective equivalence and pointwise projective relation of Randers metrics,
arXiv:1112.6143.
 
- Matveev V.S., Proof of the projective Lichnerowicz-Obata conjecture,
J. Differential Geom. 75 (2007), 459-502,
math.DG/0407337.
 
- Matveev V.S., Troyanov M.,
The Binet-Legendre metric in Finsler geometry,
arXiv:1104.1647.
 
- Rafie-Rad M., Rezaei B.,
On the projective algebra of Randers metrics of constant flag curvature,
SIGMA 7 (2011), 085, 12 pages,
arXiv:1108.6127.
 
- Wang H.C.,
On Finsler spaces with completely integrable equations of Killing,
J. London Math. Soc. 22 (1947), 5-9.
 
 
 | 
 |