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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/53898 |
| Date | 21 September 2015 |
| Creators | Hu, Jing |
| Contributors | Belegradek, Igor |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
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