The holonomy group of locally projectively flat Randers two-manifolds of constant curvature

Hubicska, Balázs and Muzsnay, Zoltán (2020) The holonomy group of locally projectively flat Randers two-manifolds of constant curvature. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 73. ISSN 0926-2245

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Abstract

In this paper, we investigate the holonomy structure of the most accessible and demonstrative 2-dimensional Finsler surfaces, the Randers surfaces. Randers metrics can be considered as the solutions of the Zermelo navigation problem. We give the classification of the holonomy groups of locally projectively flat Randers two-manifolds of constant curvature. In particular, we prove that the holonomy group of a simply connected non-Riemannian projectively flat Finsler two-manifold of constant non-zero flag curvature is maximal and isomorphic to the orientation preserving diffeomorphism group of the circle. (C) 2020 The Author(s). Published by Elsevier B.V.

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