Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle

Zoltan Muzsnay; Peter T. Nagy

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arXiv · 1210.6966

Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle

Zoltan Muzsnay·Peter T. Nagy

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Abstract

In this paper we show that the topological closure of the holonomy group of a certain class of projectively flat Finsler 2-manifolds of constant curvature is maximal, that is isomorphic to the connected component of the diffeomorphism group of the circle. This class of 2-manifolds contains the standard Funk plane of constant negative curvature and the Bryant-Shen-spheres of constant positive curvature. The result provides the first examples describing completely infinite dimensional Finslerian holonomy structures.

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BibTeX RIS

Zoltan Muzsnay, Peter T. Nagy. 2012-10-25. Finsler 2-manifolds whose holonomy group is the diffeomorphism group of the circle. https://arxiv.org/abs/1210.6966

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