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lavinia
#7
Nov29-11, 02:33 PM
Sci Advisor
P: 1,716
here is a special case. Suppose the surface has constant positive Gauss curvature.

Then radial geodesics emanating from a point all converge to the same conjugate point. This means that there is a homeomorphic image of a sphere in the surface. But then the surface itself must be a sphere.