The Schwarzian derivative on Finsler manifolds of constant curvature
| Autor: | Behroz Bidabad, F. Sedighi |
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| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics General Mathematics Rigidity (psychology) Curvature Mathematics::Geometric Topology 53C60 58B20 Constant curvature Mathematics - Analysis of PDEs Differential Geometry (math.DG) FOS: Mathematics Mathematics::Metric Geometry Development (differential geometry) Mathematics::Differential Geometry Finsler manifold Schwarzian derivative Constant (mathematics) Mathematics::Symplectic Geometry Ricci curvature Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Periodica Mathematica Hungarica. 84:346-357 |
| ISSN: | 1588-2829 0031-5303 |
| 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: | OpenAIRE |
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