Torus and sphere with positive or negative curvature

lavinia

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.

lavinia Recognitions: Science Advisor	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.