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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2013-07-24
Accepted: 2013-10-16
Published online: 2013-11-13

DOI: 10.1016/j.crma.2013.10.012

Author's affiliations:

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

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     title = {Special projective {Lichn\'erowicz{\textendash}Obata} theorem for {Randers} spaces},
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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/

References
Cited by

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[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)

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