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Some rigidity results on complete Finsler manifolds | ||
| Journal of Finsler Geometry and its Applications | ||
| مقاله 9، دوره 3، شماره 1، مهر 2022، صفحه 100-117 اصل مقاله (267.2 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2022.10415.1061 | ||
| نویسندگان | ||
| Azam Asanjarani1؛ Hengameh R. Dehkordi* 2 | ||
| 1Department of Statistics, The University of Auckland, Auckland, New Zealand | ||
| 2Center of Mathematics, Computing and Cognition - CMCC Federal University of ABC - UFABC, SP, Brazil. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Finsler metric؛ rigidity؛ constant curvature؛ second-order differential equation؛ adapted coordinate | ||
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آمار تعداد مشاهده مقاله: 208 تعداد دریافت فایل اصل مقاله: 146 |
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