On démontre quʼune métrique de Randers sur une variété de dimension est projective si et seulement si lʼalgèbre de Lie des champs de vecteurs projectifs est (localement) de dimension . Ceci peut être considéré comme un analogue du résultat correspondant en géométrie riemannienne.
It is proved that a Randers metric on a manifold of dimension is projective if and only if the Lie algebra of projective vector fields has (locally) dimension . This can be regarded as an analogue of the corresponding result in Riemannian geometry.
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@article{CRMATH_2012__350_5-6_281_0, author = {Rafie-Rad, Mehdi and Rezaei, Bahman}, title = {On the projective {Randers} metrics}, journal = {Comptes Rendus. Math\'ematique}, pages = {281--283}, publisher = {Elsevier}, volume = {350}, number = {5-6}, year = {2012}, doi = {10.1016/j.crma.2012.02.010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.02.010/} }
TY - JOUR AU - Rafie-Rad, Mehdi AU - Rezaei, Bahman TI - On the projective Randers metrics JO - Comptes Rendus. Mathématique PY - 2012 SP - 281 EP - 283 VL - 350 IS - 5-6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.02.010/ DO - 10.1016/j.crma.2012.02.010 LA - en ID - CRMATH_2012__350_5-6_281_0 ER -
%0 Journal Article %A Rafie-Rad, Mehdi %A Rezaei, Bahman %T On the projective Randers metrics %J Comptes Rendus. Mathématique %D 2012 %P 281-283 %V 350 %N 5-6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.02.010/ %R 10.1016/j.crma.2012.02.010 %G en %F CRMATH_2012__350_5-6_281_0
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://archive.numdam.org/articles/10.1016/j.crma.2012.02.010/
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