Special projective Lichnérowicz–Obata theorem for Randers spaces

Mehdi Rafie-Rad

doi:10.1016/j.crma.2013.10.012

Differential geometry

Special projective Lichnérowicz–Obata theorem for Randers spaces
[Le théorème projectif resteint de Lichnérowicz–Obata sur les espaces de Randers]

Présenté par : the Editorial Board

Mehdi Rafie-Rad ^1,²

¹ School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
² Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran

Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 927-930.

Résumé
Abstract

On prouve que, soit chaque champ projectif de vecteurs sur un espace de Randers $(M, F = α + β)$ est conforme à la métrique riemanienne $α^{2} - β^{2}$ , soit F est à S-courbure isotrope. Ce résultat est appliqué à lʼétablissement dʼun théorème de type de Lichnérowicz–Obata sur les variétés fermées de Randers.

It is proved that either every special projective vector field V on a Randers space $(M, F = α + β)$ is a conformal vector field of the Riemannian metric $α^{2} - β^{2}$ , or F is of isotropic S-curvature. This result is applied to establish a projective Lichnérowicz–Obata-type result on the closed manifolds with generic Randers metrics.

Reçu le : 2013-07-24
Accepté le : 2013-10-16
Publié le : 2013-11-13

DOI : 10.1016/j.crma.2013.10.012

Affiliations des auteurs :

Mehdi Rafie-Rad ^{1, 2}

@article{CRMATH_2013__351_23-24_927_0,
     author = {Mehdi Rafie-Rad},
     title = {Special projective {Lichn\'erowicz{\textendash}Obata} theorem for {Randers} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {927--930},
     publisher = {Elsevier},
     volume = {351},
     number = {23-24},
     year = {2013},
     doi = {10.1016/j.crma.2013.10.012},
     language = {en},
}

TY  - JOUR
AU  - Mehdi Rafie-Rad
TI  - Special projective Lichnérowicz–Obata theorem for Randers spaces
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 927
EP  - 930
VL  - 351
IS  - 23-24
PB  - Elsevier
DO  - 10.1016/j.crma.2013.10.012
LA  - en
ID  - CRMATH_2013__351_23-24_927_0
ER  -

%0 Journal Article
%A Mehdi Rafie-Rad
%T Special projective Lichnérowicz–Obata theorem for Randers spaces
%J Comptes Rendus. Mathématique
%D 2013
%P 927-930
%V 351
%N 23-24
%I Elsevier
%R 10.1016/j.crma.2013.10.012
%G en
%F CRMATH_2013__351_23-24_927_0

Mehdi Rafie-Rad. Special projective Lichnérowicz–Obata theorem for Randers spaces. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 927-930. doi : 10.1016/j.crma.2013.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.012/

Bibliographie
Cité par

[1] H. Akbar-Zadeh Champs de vecteurs projectifs sur le fibré unitaire, J. Math. Pures Appl., Volume 65 (1986), pp. 47-79

[2] X. Chen; X. Mo; Z. Shen On the flag curvature of Finsler metrics of scalar curvature, J. Lond. Math. Soc., Volume 68 (2003), pp. 762-780

[3] X. Chen; Z. Shen Randers metrics with special curvature properties, Osaka J. Math., Volume 40 (2003), pp. 87-101

[4] V.S. Matveev On projective equivalence and pointwise projective relation of Randers metrics, Int. J. Math., Volume 23 (2012) no. 9, p. 1250093 (14 pages)

[5] M. Rafie-Rad Some new characterizations of projective Randers metrics with constant S-curvature, J. Geom. Phys., Volume 9 (2012) no. 4, pp. 272-278

[6] M. Rafie-Rad Special projective algebra of Randers metrics of constant S-curvature, Int. J. Geom. Methods Mod. Phys., Volume 6 (2012) no. 2

[7] M. Rafie-Rad; B. Rezaei On the projective algebra of Randers metrics of constant flag curvature, SIGMA, Volume 7 (2011), p. 085 (12 pages)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

On the projective Randers metrics

Mehdi Rafie-Rad; Bahman Rezaei

C. R. Math (2012)

Homogeneous Einstein–Randers spaces of negative Ricci curvature

Shaoqiang Deng; Zixin Hou

C. R. Math (2009)