Return to search

Cohomogeneity One Einstein Metrics on Vector Bundles

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)

Identiferoai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/24886
Date January 2019
CreatorsChi, Hanci
ContributorsWang, McKenzie, Mathematics and Statistics
Source SetsMcMaster University
LanguageEnglish
Detected LanguageEnglish
TypeThesis

Page generated in 0.0019 seconds