I have been searching for a while for a proof of the following fact: For a closed Riemannian manifold, all of whose sectional curvatures are negative, each free homotopy class of loops contains a unique closed geodesic. I found a proof for surfaces of constant negative curvature in Stillwell's "Geometry of Surfaces" but I haven't been able to find a source which proves this in greater generality.
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
