Finsler 2-manifolds with maximal holonomy group of infinite dimension

In this paper we are investigating the holonomy structure of Finsler 2-manifolds. 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 diffeomorphi...

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Bibliographic Details
Published inDifferential geometry and its applications Vol. 39; pp. 1 - 9
Main Authors Muzsnay, Zoltán, Nagy, Péter T.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2015
Subjects
Finsler geometry
Groups of diffeomorphisms
Holonomy
Infinite-dimensional Lie groups
Lie algebras of vector fields
17B66
Finsler geometry
53B40
58D05
Groups of diffeomorphisms
Holonomy
Lie algebras of vector fields
22E65
Infinite-dimensional Lie groups
53C29
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Summary:In this paper we are investigating the holonomy structure of Finsler 2-manifolds. 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.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2015.01.001