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- W3009023624 abstract "Thurston, in 1986, discovered that the Schwarzian derivative has mysterious properties similar to the curvature on a manifold. After his work, there are several approaches to develop this notion on Riemannian manifolds. Here, a tensor field is identified in the study of global conformal diffeomorphisms on Finsler manifolds as a natural generalization of the Schwarzian derivative. Then, a natural definition of a Mobius mapping on Finsler manifolds is given and its properties are studied. In particular, it is shown that Mobius mappings are mappings that preserve circles and vice versa. Therefore, if a forward geodesically complete Finsler manifold admits a Mobius mapping, then the indicatrix is conformally diffeomorphic to the Euclidean sphere $ S^{n-1}$ in $ mathbb{R}^n $. In addition, if a forward geodesically complete absolutely homogeneous Finsler manifold of scalar flag curvature admits a non-trivial change of Mobius mapping, then it is a Riemannian manifold of constant sectional curvature." @default.
- W3009023624 created "2020-03-06" @default.
- W3009023624 creator A5042261493 @default.
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- W3009023624 date "2020-02-19" @default.
- W3009023624 modified "2023-10-01" @default.
- W3009023624 title "The Schwarzian derivative and conformal transformation on Finsler manifolds" @default.
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