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http://dx.doi.org/10.4134/JKMS.j190436

THE SCHWARZIAN DERIVATIVE AND CONFORMAL TRANSFORMATION ON FINSLER MANIFOLDS  

Bidabad, Behroz (Faculty of Mathematics and Computer Science Amirkabir University of Technology)
Sedighi, Faranak (Faculty of Mathematics Payame Noor University of Tehran)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 873-892 More about this Journal
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 Sn-1 in ℝn. 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.
Keywords
Finsler; Schwarzian; Mobius; conformal; projective; concircular;
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Times Cited By KSCI : 2  (Citation Analysis)
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