Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/18961
Title: | Bundle Construction of Einstein Manifolds |
Authors: | Chen, Dezhong |
Advisor: | Wang, M. Y. |
Department: | Mathematics |
Keywords: | bundle, construction, Einstein, manifolds, geometric, properties, dimensions |
Publication Date: | Aug-2010 |
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> |
URI: | http://hdl.handle.net/11375/18961 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Chen_Dezhong_2010Aug_Ph.D..pdf | 3.78 MB | Adobe PDF | View/Open |
Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.