Rigidity from the strong unstable foliation for higher-dimensional Anosov and partially hyperbolic flows

Recently Burniol Clotet proved that two transitive Anosov flows on 3-manifolds with equivalent strong unstable foliations must be conjugate up to time rescaling. We further explore the mechanism of Burniol Clotet’s argument and treat the case of higher-dimensional Anosov flows and their isometric extensions by compact Lie groups.