The Blaschke conjecture states that the only Wiedersehen surfaces are the standard round spheres. The conjecture
was proven by combining the Berger-Kazdan
comparison theorem with A. Weinstein's results for 
even and C. T. Yang's
for 
odd. Green (1963) obtained the first proof
of the Blaschke's conjecture in the two-dimensional
case.
A broader metric formulation concerns a closed connected smooth Riemannian manifold whose global injectivity radius equals its diameter.
