On the ergodicity of the frame flow on even-dimensional manifolds
Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
It is known that the frame flow on a closed n-dimensional Riemannian manifold with negative sectional curvature is ergodic if nis odd and n≠7. In this paper we study its ergodicity in the remaining cases. For neven and n≠8,134, we show that: if n≡2mod 4 or n=4, the frame flow is ergodic if the manifold is ∼0.3-pinched, if n≡0mod 4, it is ergodic if the manifold is ∼0.6-pinched. In the three dimensions n=7,8,134, the respective pinching bounds that we need in order to prove ergodicity are 0.4962..., 0.6212..., and 0.5788.... This is a significant improvement over the previously known results and a step forward towards solving a long-standing conjecture of Brin asserting that 0.25-pinched even-dimensional manifolds have an ergodic frame flow.
Description
Keywords
Citation
Collections
Endorsement
Review
Supplemented By
Referenced By
Creative Commons license
Except where otherwised noted, this item's license is described as CC BY