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Higher rank rigidity for Berwald spaces

Part of: Symplectic geometry, contact geometry Dynamical systems with hyperbolic behavior Global differential geometry

Published online by Cambridge University Press:  18 December 2018

WEISHENG WU
WEISHENG WU*
Affiliation:
Department of Applied Mathematics, College of Science, China Agricultural University, Beijing, 100083, PR China email wuweisheng@cau.edu.cn
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Abstract

We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded non-positive flag curvature with rank at least two whose universal cover is irreducible is a locally symmetric space or a locally Minkowski space.

Keywords

higher rank rigiditygeodesic flowBerwald spacesFinsler spacesnon-positive flag curvature

MSC classification

Primary: 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Secondary: 53D25: Geodesic flows 53C24: Rigidity results
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 7 , July 2020 , pp. 1991 - 2016
Copyright
© Cambridge University Press, 2018

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