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# Spherical Rank Rigidity and Blaschke Manifolds

@inproceedings{Shankar2003SphericalRR, title={Spherical Rank Rigidity and Blaschke Manifolds}, author={Krishnan Shankar and RALF SPATZIER and BURKHARD WILKING}, year={2003} }

- Published 2003

By the Rauch comparison theorem we know that along any geodesic there cannot be a conjugate point before π. The well known equality discussion implies that for any normal geodesic c : [0, π] → M there exists a spherical Jacobi field i.e., a Jacobi field of the form J(t) = sin(t)E(t) where E is a parallel vector field (see for instance [Chav93, Theorem 2.15]). This latter characterization is analogous to the notions of (upper) Euclidean rank and (upper) hyperbolic rank studied by several people… CONTINUE READING