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. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/24886 |
| Date | January 2019 |
| Creators | Chi, Hanci |
| Contributors | Wang, McKenzie, Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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