Simplicity of the Lyapunov spectrum for classes of Anosov flows

For k≥2 , we prove that in a C¹ -open and C^k -dense set of some classes of C^k -Anosov flows, all Lyapunov exponents have multiplicity one with respect to appropriate measures. The classes are geodesic flows with equilibrium states of Holder-continuous potentials, volume-preserving flows, and all fiber-bunched Anosov flows with equilibrium states of Holder-continuous potentials.