Contents Online

# Mathematical Research Letters

## Volume 4 (1997)

### Number 6

### On the regularity of the Anosov splitting for twisted geodesic flows

Pages: 871 – 888

DOI: http://dx.doi.org/10.4310/MRL.1997.v4.n6.a7

#### Author

#### Abstract

Let $M$ denote a closed Riemannian manifold whose geodesic flow is Anosov. Given a real number $\lambda$ and a smooth one form $\theta$, consider the twisted geodesic flow obtained by twisting the canonical symplectic structure by the lift of $\lambda d\theta$ to the tangent bundle of $M$. For $\lambda$ in a certain open interval around the origin the twisted flow remains Anosov. We show that the Anosov splitting of the twisted geodesic flow is never of class $C^{1}$ unless $\lambda=0$.