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}
}
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

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