2-Frame flow dynamics and hyperbolic rank-rigidity in nonpositive curvature
2-Frame flow dynamics and hyperbolic rank-rigidity in nonpositive curvature
This paper presents hyperbolic rank-rigidity results for nonpositivelycurved spaces of rank 1. Let $M$ be a compact, rank-1 manifold withnonpositive sectional curvature and suppose that along every geodesic in$M$ there is a parallel vector field making curvature $-a^2$ with thegeodesic direction. We prove that $M$ has constant curvature equal to$-a^2$ …