Weakly conformal Finsler geometry

作者：Rafie Rad Mehdi^*

来源：Mathematische Nachrichten, 2014, 287(14-15): 1745-1755.

DOI：10.1002/mana.201300099

• Finsler metric
• Randers metric
• conformal geometry

An extension of conformal equivalence for Finsler metrics is introduced and called weakly conformal equivalence and is used to define the weakly conformal transformations. The conformal Lichnerowicz-Obata conjecture is refined to weakly conformal Finsler geometry. It is proved that: If X is a weakly conformal complete vector field on a connected Finsler space (M, F) of dimension n >= 2, then, at least one of the following statements holds: (a) There exists a Finsler metric F-1 weakly conformally equivalent to F such that X is a Killing vector field of the Finsler metric, (b) M is diffeomorphic to the sphere S-n and the Finsler metric is weakly conformally equivalent to the standard Riemannian metric on S-n, and (c) M is diffeomorphic to the Euclidean space R-n and the Finsler metric F is weakly conformally equivalent to a Minkowski metric on R-n. The considerations invite further dynamics on Finsler manifolds.

• 出版日期2014-10