Journal of Differential Geometry

Quasigeodesic flows and Möbius-like groups

Steven Frankel

Abstract

If M is a hyperbolic 3-manifold with a quasigeodesic flow, then we show that $\pi_1(M)$ acts in a natural way on a closed disc by homeomorphisms. Consequently, such a flow either has a closed orbit or the action on the boundary circle is Möbius-like but not conjugate into $PSL(2,\mathbb{R})$.We conjecture that the latter possibility cannot occur.

Article information

Source
J. Differential Geom., Volume 93, Number 3 (2013), 401-429.

Dates
First available in Project Euclid: 26 February 2013

https://projecteuclid.org/euclid.jdg/1361844940

Digital Object Identifier
doi:10.4310/jdg/1361844940

Mathematical Reviews number (MathSciNet)
MR3024301

Zentralblatt MATH identifier
1279.53063

Citation

Frankel, Steven. Quasigeodesic flows and Möbius-like groups. J. Differential Geom. 93 (2013), no. 3, 401--429. doi:10.4310/jdg/1361844940. https://projecteuclid.org/euclid.jdg/1361844940