Some rigidity results on complete Finsler manifolds
Publish Year: 1401
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JFGA-3-1_009
تاریخ نمایه سازی: 18 آبان 1402
Abstract:
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 simply connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to a 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.
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Authors
Azam Asanjarani
Department of Statistics, The University of Auckland, Auckland, New Zealand
Hengameh R. Dehkordi
Center of Mathematics, Computing and Cognition - CMCC Federal University of ABC - UFABC, SP, Brazil.