no. 21-22
Differential Geometry
On compact Finsler spaces of positive constant curvature
[Sur les espaces finsleriennes compacts à courbure positive constante]

Présenté par : the Editorial Board

Bidabad, Behroz1
1 Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran
Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1191-1194.

Un espace de Finsler de dimension n (n⩾2), simplement connexe, compact, non-borné et à courbure sectionnelle positive constante est conformément homéomorphe à une n-sphère dʼun espace euclidien Rn+1.

An n-dimensional (n⩾2) simply connected, compact without boundary Finsler space of positive constant sectional curvature is conformally homeomorphic to an n-sphere in the Euclidean space Rn+1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.014
Bidabad, Behroz 1

1 Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran 
@article{CRMATH_2011__349_21-22_1191_0,
     author = {Bidabad, Behroz},
     title = {On compact {Finsler} spaces of positive constant curvature},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1191--1194},
     publisher = {Elsevier},
     volume = {349},
     number = {21-22},
     year = {2011},
     doi = {10.1016/j.crma.2011.10.014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.10.014/}
}
TY  - JOUR
AU  - Bidabad, Behroz
TI  - On compact Finsler spaces of positive constant curvature
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 1191
EP  - 1194
VL  - 349
IS  - 21-22
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2011.10.014/
DO  - 10.1016/j.crma.2011.10.014
LA  - en
ID  - CRMATH_2011__349_21-22_1191_0
ER  - 
%0 Journal Article
%A Bidabad, Behroz
%T On compact Finsler spaces of positive constant curvature
%J Comptes Rendus. Mathématique
%D 2011
%P 1191-1194
%V 349
%N 21-22
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2011.10.014/
%R 10.1016/j.crma.2011.10.014
%G en
%F CRMATH_2011__349_21-22_1191_0
Bidabad, Behroz. On compact Finsler spaces of positive constant curvature. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1191-1194. doi : 10.1016/j.crma.2011.10.014. http://www.numdam.org/articles/10.1016/j.crma.2011.10.014/

[1] Akbar-Zadeh, H. Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Bull. Cl. Sci. (5), Volume 74 (1988), pp. 281-322

[2] Asanjarani, A.; Bidabad, B. Classification of complete Finsler manifolds through a second order differential equation, Differential Geom. Appl., Volume 26 (2008), pp. 434-444

[3] Bao, D.; Chern, S.S.; Shen, Z. Riemann–Finsler Geometry, Springer-Verlag, 2000

[4] Bidabad, B. Complete Finsler manifolds and adapted coordinates, Balkan J. Geom. Appl., Volume 14 (2009) no. 1, pp. 21-29

[5] B. Bidabad, Z. Shen, Circle-preserving transformations on Finsler spaces, in press.

[6] Lehmann, D. Séminaire Ehresmann, Topologie et géometrie différentielle, Volume 6 (1964)

[7] Shen, Z. Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, Dordrecht, 2001

[8] Tashiro, Y. Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc., Volume 117 (1965), pp. 251-275

Cité par Sources :