Using Homogeneous Structures to Measure Homogeneity of Riemannian Manifolds
Author
MacLaughlin, AndrewIssue Date
2018Advisor
Glickenstein, David
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The University of Arizona.Rights
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.Abstract
A result of Ambrose and Singer characterizes connected, locally homogeneous spaces by the existence of one or more special affine connections, called homogeneous structures. In this dissertation, we use this result to define an energy on the class of all connected, compact Riemannian manifolds which is equal to zero if a manifold is locally homogeneous. We further provide refinements to this energy for two and three-dimensional manifolds so that the energy is equal to zero if and only if a manifold is locally homogeneous.Type
textElectronic Dissertation
Degree Name
Ph.D.Degree Level
doctoralDegree Program
Graduate CollegeMathematics