Premium
Weakly conformal Finsler geometry
Author(s) -
RafieRad Mehdi
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300099
Subject(s) - mathematics , conformal map , finsler manifold , minkowski space , equivalence (formal languages) , pure mathematics , diffeomorphism , euclidean space , metric (unit) , vector field , mathematical analysis , mathematical physics , geometry , operations management , scalar curvature , curvature , economics
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 dimensionn ≥ 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 sphereS nand the Finsler metric is weakly conformally equivalent to the standard Riemannian metric onS n , and (c) M is diffeomorphic to the Euclidean spaceR nand the Finsler metric F is weakly conformally equivalent to a Minkowski metric onR n . The considerations invite further dynamics on Finsler manifolds.