On embedded spheres of affine manifolds
| dc.contributor.advisor | Goldman, William M | en_US |
| dc.contributor.author | Wu, Weiqiang | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2012-10-11T05:54:05Z | |
| dc.date.available | 2012-10-11T05:54:05Z | |
| dc.date.issued | 2012 | en_US |
| dc.description.abstract | This paper studies certain embedded spheres in closed affine manifolds. For n greater than or equal to 3, we investigate the dome bodies in a closed affine n-manifold M with its boundary homeomorphic to a sphere under the assumption that a developing map restricted to a component of the boundary of hat{M} is an embedding onto a strictly convex sphere in A^n. By using the recurrent property of an incomplete geodesic we show that dome bodies are compact. Then a maximal dome body is a closed solid ball bounded by a component of the boundary of hat{M}, and hence equals hat{M} . The main theorem is that the standard ball in an affine space can only bound one compact affine manifold inside, namely the solid ball. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1903/13184 | |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | affine structures | en_US |
| dc.subject.pquncontrolled | developing and holonomy | en_US |
| dc.subject.pquncontrolled | dome bodies | en_US |
| dc.subject.pquncontrolled | incomplete geodesics | en_US |
| dc.title | On embedded spheres of affine manifolds | en_US |
| dc.type | Dissertation | en_US |
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