Anosov flows induced by partially hyperbolic \(\Sigma\)-geodesic flows. (Q2766497)

The authors construct a class of examples of partially hyperbolic systems. They consider a non-integrable codimension 1 distribution \(\Sigma\) on the tangent-bundle of a compact Riemannian manifold. Associated to this distribution they define a generalized geodesic flow determined by the equation \(\nabla_{\dot q}\dot q+b(\dot q,\dot q)=0\), where \(\nabla\) is the Levi-Civita connection and \(B\) is the second fundamental form of \(\Sigma\). If the flow conserves volume and \(\Sigma\) is constant umbilical then the flow is partially hyperbolic provided that \(\Sigma\) has sufficiently negative sectional curvature.