Some Rigidity Results on Complete Finsler Manifolds

Autor:	Asanjarani, Azam, Dehkordi, Hengameh R.
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry 53C60 58B20
Druh dokumentu:	Working Paper
Popis:	We provide an extension of Obata's theorem to Finsler geometry and establish some rigidity results based on a second order differential equation. Mainly, we prove that every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to an Euclidean sphere endowed with a certain Finsler metric and vice versa. Based on these results, we present a classification of Finsler manifolds which admit a transnormal function. Specifically, we show that if a complete Finsler manifold admits a transnormal function with exactly two critical points, then it is homeomorphic to a sphere. Comment: arXiv admin note: substantial text overlap with arXiv:0711.1587
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.11027 Zobrazit plný text záznamu View this record from Arxiv