Blaschke Conjecture

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.

REFERENCES:

Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.

Green, L. W., "Auf Wiedersehensflächen." Ann. Math. 78, 289-299, 1963.