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.
Blaschke Conjecture
See also
Wiedersehen SurfaceExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Blaschke ConjectureCite this as:
Weisstein, Eric W. "Blaschke Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BlaschkeConjecture.html