1403/01/10
مهدی رفیعی راد

مهدی رفیعی راد

مرتبه علمی: دانشیار
ارکید: 0000-0002-8214-3835
تحصیلات: دکترای تخصصی
اسکاپوس: 23493274700
دانشکده: دانشکده علوم ریاضی
نشانی:
تلفن: 01135302464

مشخصات پژوهش

عنوان
Weakly conformal Finsler geometry
نوع پژوهش
JournalPaper
کلیدواژه‌ها
Finsler metric, Randers metric, conformal geometry
سال
2014
مجله MATHEMATISCHE NACHRICHTEN
شناسه DOI
پژوهشگران Mehdi Rafie-Rad

چکیده

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 F1 weakly conformally equivalent to F such that X is a Killing vector field of the Finsler metric, (b) M is diffeomorphic to the sphere Sn and the Finsler metric is weakly conformally equivalent to the standard Riemannian metric on Sn , and (c) M is diffeomorphic to the Euclidean space Rn and the Finsler metric F is weakly conformally equivalent to a Minkowski metric on Rn . The considerations invite further dynamics on Finsler manifolds.