The Schwarzian derivative on Finsler manifolds of constant curvature

Autor:	Bidabad, Behroz, Sedighi, Faranak
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 53C60 58B20
Druh dokumentu:	Working Paper
DOI:	10.1007/s10998-021-00411-z
Popis:	Lagrange introduced the notion of Schwarzian derivative and Thurston discovered its mysterious properties playing a role similar to that of curvature on Riemannian manifolds. Here we continue our studies on the development of the Schwarzian derivative on Finsler manifolds. First, we obtain an integrability condition for the M\"{o}bius equations. Then we obtain a rigidity result as follows; Let $(M, F)$ be a connected complete Finsler manifold of positive constant Ricci curvature. If it admits non-trivial M\"{o}bius mapping, then $M$ is homeomorphic to the $n$-sphere. Finally, we reconfirm Thurston's hypothesis for complete Finsler manifolds and show that the Schwarzian derivative of a projective parameter plays the same role as the Ricci curvature on theses manifolds and could characterize a Bonnet-Mayer-type theorem. Comment: 12 pages. Periodica Mathematica Hungarica, (2021)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.00480 Zobrazit plný text záznamu View this record from Arxiv