The Myers-Steenrod theorem for Finsler manifolds of low regularity

Abstract

We prove a version of Myers-Steenrod's theorem for Finsler manifolds under minimal regularity hypothesis. In particular we show that an isometry between $C^{k,\alpha }$-smooth (or partially smooth) Finsler metrics, with $k+\alpha >0$, $k\in \mathbb{N}\cup \{0\}$, and $0\le \alpha \le 1$ is necessary a diffeomorphism of class $C^{k+1,\alpha }$. A generalisation of this result to the case of Finsler 1-quasiconformal mapping is given. The proofs are based on the reduction of the Finlserian problems to Riemannian ones with the help of the the Binet-Legendre metric.

14 pages

References in corpus (1)

• Completeness and incompleteness of the Binet-Legendre Metric

Cited by in corpus (7)

• Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
• Coarse and fine geometry of the Thurston metric
• Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form
• Local Rigidity of Teichmüller space with Thurston metric
• Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics
• Conformal harmonic coordinates
• If a Minkowski billiard is projective, it is the standard billiard