On compact Finsler spaces of positive constant curvature

Behroz Bidabad

doi:10.1016/j.crma.2011.10.014

Differential Geometry

On compact Finsler spaces of positive constant curvature
[Sur les espaces finsleriennes compacts à courbure positive constante]

Présenté par : the Editorial Board

Behroz Bidabad ¹

¹ Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran

Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1191-1194.

Résumé
Abstract

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 $R^{n + 1}$ .

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 $R^{n + 1}$ .

Reçu le : 2011-09-05
Accepté le : 2011-10-18
Publié le : 2011-11-01

DOI : 10.1016/j.crma.2011.10.014

Affiliations des auteurs :

Behroz Bidabad ¹

¹ Department of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran

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     author = {Behroz Bidabad},
     title = {On compact {Finsler} spaces of positive constant curvature},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1191--1194},
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     volume = {349},
     number = {21-22},
     year = {2011},
     doi = {10.1016/j.crma.2011.10.014},
     language = {en},
}

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Behroz Bidabad. On compact Finsler spaces of positive constant curvature. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1191-1194. doi : 10.1016/j.crma.2011.10.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.014/

Bibliographie
Cité par

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

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

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

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

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

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

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