Author:
Gogolev Andrey,Hertz Federico Rodriguez
Abstract
UDC 515.12
We apply the technique of matching functions in the setting of contact Anosov flows satisfying a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman and Ornstein [Ergodic Theory Dynam. Syst., <strong>7</strong>, No. 1, 49–72 (1987)]. Namely, we show that if two Anosov flow of this kind are
C
0
conjugate, then they are
C
r
conjugate for some
r
∈
[
1,2
)
or even
C
∞
conjugate under certain additional assumptions. This, for example, applies to geodesic flows on compact Riemannian manifolds of
1
/
4
-pinched negative sectional curvature. We can also use our result to recover Hamendstўаdt's marked length spectrum rigidity result for real hyperbolic manifolds.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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