Hyperbolic rank rigidity for manifolds of $\frac{1}{4}$-pinched negative curvature

Chris Connell, Thang Nguyen, Ralf Spatzier

A Riemannian manifold $M$ has higher hyperbolic rank if every geodesic has a perpendicular Jacobi field making sectional curvature -1 with the geodesic. If in addition, the section…