Abstract
A Riemannian manifold with upper curvature bound 1
is said to have positive spherical rank if any geodesic
$c$ has a conjugate point at $pi$.
It is easy to see that this notion is analogous
to the notions of Euclidean and hyperbolic rank for manifolds
with upper curvature bound 0 and -1, respectively.
In a joint work with Krishnan Shankar and Ralf Spatzier we
prove that a manifold with positive spherical rank is locally
symmetric.
Contact person:Jørgen Ellegaard Andersen.