Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic

2022/10/17 by Fenley, Sergio R
#37C27 #37C86 #37D05 #37D20 #37E10 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 57R30 #Secondary: 53C12

paper · doi:10.48550/arxiv.2210.09238

Abstract

The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic three manifold, and the existence of group invariant Peano curves associated with any such flow.

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