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This paper presents hyperbolic rank rigidity results for rank 1,nonpositively curved spaces. 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 the geodesicdirection. We prove that $M$ has constant curvature equal to $-a^2$ if $M$ isodd dimensional, or if $M$ is even dimensional and has sectional curvaturepinched as follows: $-\Lambda^2 < K < -\lambda^2$ where $\lambda/\Lambda >>.93$. When $-a^2$ is the upper curvature bound this gives a shorter proof ofthe hyperbolic rank rigidity theorem of Hamenst\"{a}dt, subject to the pinchingcondition in even dimension; in all other cases it is a new result. We alsopresent a rigidity result using only an assumption on maximal Lyapunovexponents in direct analogy with work done by Connell. The proof of the maintheorem is simplified considerably by assuming strict negative curvature; infact, in all dimensions but 7 and 8 it is then an immediate consequence ofergodicity of the $(dim(M)-1)$-frame flow. In these exceptional dimensions,recourse to the dynamics of the 2-frame flow must be made and the scheme ofproof developed there can be generalized to deal with rank 1, nonpositivelycurved spaces.

2-Frame flow dynamics and hyperbolic rank rigidity in nonpositive curvature