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Complete nonnegatively curved spheres and planesHu, Jing 21 September 2015 (has links)
We study the space of complete Riemannian metrics of nonnegative curvature on the sphere equipped with C^{k+\alpha} topology. We show the space is homogenous for k>=2. If k is infinite, we show that the space is homeomorphic to the separable Hilbert space. We also prove for finite k, the space minius any compact subset is weakly contractible.
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