Almost All Finsler Metrics have Infinite Dimensional Holonomy Group

We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.

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Bibliographic Details
Published in:	The Journal of geometric analysis Vol. 31; no. 6; pp. 6067 - 6079
Main Authors:	Hubicska, B., Matveev, V. S., Muzsnay, Z.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-06-2021 Springer Nature B.V
Subjects:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics 17B66 Finsler geometry 53B40 Holonomy 22E65 Curvature Algebras of vector fields 53C29
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Description
Summary:	We show that the set of Finsler metrics on a manifold contains an open everywhere dense subset of Finsler metrics with infinite-dimensional holonomy groups.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-020-00517-9