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http://hdl.handle.net/11375/18961
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DC Field | Value | Language |
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dc.contributor.advisor | Wang, M. Y. | - |
dc.contributor.author | Chen, Dezhong | - |
dc.date.accessioned | 2016-03-16T18:17:58Z | - |
dc.date.available | 2016-03-16T18:17:58Z | - |
dc.date.issued | 2010-08 | - |
dc.identifier.uri | http://hdl.handle.net/11375/18961 | - |
dc.description.abstract | <p> The aim of this thesis is to construct some smooth Einstein manifolds with nonzero Einstein constant, and then to investigate their topological and geometric properties.</p> <p> In the negative case, we are able to construct conformally compact Einstein metrics on 1. products of an arbitrary closed Einstein manifold and a certain even-dimensional ball bundle over products of Hodge Kähler-Einstein manifolds, 2. certain solid torus bundles over a single Fano Kähler-Einstein manifold. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As by-products, we obtain many Riemannian manifolds with vanishing Q-curvature.</p> <p> In the positive case, we are able to construct complete Einstein metrics on certain 3-sphere bundles over a Fano Kähler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base manifold is the complex projective plane.</p> | en_US |
dc.language.iso | en_US | en_US |
dc.subject | bundle, construction, Einstein, manifolds, geometric, properties, dimensions | en_US |
dc.title | Bundle Construction of Einstein Manifolds | en_US |
dc.type | Thesis | en_US |
dc.contributor.department | Mathematics | en_US |
dc.description.degreetype | Thesis | en_US |
dc.description.degree | Doctor of Philosophy (PhD) | en_US |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Chen_Dezhong_2010Aug_Ph.D..pdf | 3.78 MB | Adobe PDF | View/Open |
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