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http://hdl.handle.net/11375/24886
Title: | Cohomogeneity One Einstein Metrics on Vector Bundles |
Authors: | Chi, Hanci |
Advisor: | Wang, McKenzie |
Department: | Mathematics and Statistics |
Keywords: | Einstein metric;Special holonomy;Cohomogeneity one;Vector bundle |
Publication Date: | 2019 |
Abstract: | This thesis studies the construction of noncompact Einstein manifolds of cohomogeneity one on some vector bundles. Cohomogeneity one vector bundle whose isotropy representation of the principal orbit G/K has two inequivalent irreducible summands has been studied in [Böh99][Win17]. However, the method applied does not cover all cases. This thesis provides an alternative construction with a weaker assumption of G/K admits at least one invariant Einstein metric. Some new Einstein metrics of Taub-NUT type are also constructed. This thesis also provides construction of cohomogeneity one Einstein metrics for cases where G/K is a Wallach space. Specifically, two continuous families of complete smooth Einstein metrics are constructed on vector bundles over CP2, HP2 and OP2 with respective principal orbits the Wallach spaces SU(3)/T2, Sp(3)/(Sp(1)Sp(1)Sp(1)) and F4/Spin(8). The first family is a 1-parameter family of Ricci-flat metrics. All the Ricci- flat metrics constructed have asymptotically conical limits given by the metric cone over a suitable multiple of the normal Einstein metric. All the Ricci-flat metrics constructed have generic holonomy except that the complete metric with G2 holonomy discovered in [BS89][GPP90] lies in the interior of the 1-parameter family on manifold in the first case. The second family is a 2-parameter family of Poincaré–Einstein metrics. |
URI: | http://hdl.handle.net/11375/24886 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Cohomogeneity One Einstein Metrics on Vector Bundles.pdf | 3.09 MB | Adobe PDF | View/Open |
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