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<p>The main result is that if an Anosov flow in a closed hyperbolic three manifold is not <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> <EquationSource Format="TEX">$\mbox{${\mathbb{R}}$}$</EquationSource> </InlineEquation>-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.</p>

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Non ℝ-Covered Anosov Flows in Hyperbolic 3-Manifolds Are Quasigeodesic

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Sergio R. Fenley

摘要

The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R $\mbox{${\mathbb{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.