Problem 11

Nonalgebraic Anosov diffeos. Classify 3-dimensional Anosov flows; Is the variable curvature surface geodesic flow conjugate to constant curvature?

Comments

  • Ledrappier (2016-11-14 11:38:00 -0800 -0800):
  • rpotrie (2017-06-13 18:16:46 -0700 -0700):

    See the introduction of https://arxiv.org/pdf/1505.06259.pdf for a quick account on results about classification of Anosov flows in dimension 3.

  • Steve Hurder (2017-06-24 04:55:07 -0700 -0700):

    The geodesic flow for a variable, non-constant negative curvature surface is never $C^2$ conjugate to a constant curvature flow. See the papers by [ghys1987flotsanosov] and [hurderkatok1991anosovflows].

  • rpotrie (2017-06-29 12:02:26 -0700 -0700):

    For non-algebraic Anosov diffeomorphisms. See Farrell, F. T.; Jones, L. E. Anosov diffeomorphisms constructed from π1Diff(Sn). Topology 17 (1978), no. 3, 273–282.