Differential geometry
Special projective Lichnérowicz–Obata theorem for Randers spaces
Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 927-930.

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 α2β2, 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 α2β2, 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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.012
Rafie-Rad, Mehdi 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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Rafie-Rad, Mehdi. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.10.012/

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