Geodesic
Differential Geometry/Mathematical Physics
On the projective Randers metrics
[Sur les métriques de Randers projectives]

Présenté par : the Editorial Board

Rafie-Rad, Mehdi1, 2 ; Rezaei, Bahman3
1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
3 Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran
Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 281-283.

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It is proved that a Randers metric F=α+β on a manifold of dimension n⩾3 is projective if and only if the Lie algebra of projective vector fields p(M,F) has (locally) dimension n(n+2). This can be regarded as an analogue of the corresponding result in Riemannian geometry.

On démontre quʼune métrique de Randers F=α+β sur une variété de dimension n⩾3 est projective si et seulement si lʼalgèbre de Lie des champs de vecteurs projectifs p(M,F) est (localement) de dimension n(n+2). Ceci peut être considéré comme un analogue du résultat correspondant en géométrie riemannienne.

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DOI : 10.1016/j.crma.2012.02.010

Rafie-Rad, Mehdi 1, 2 ; Rezaei, Bahman 3

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
2 School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
3 Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran 
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Rafie-Rad, Mehdi; Rezaei, Bahman. On the projective Randers metrics. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 281-283. doi : 10.1016/j.crma.2012.02.010. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2012.02.010/

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