Using Homogeneous Structures to Measure Homogeneity of Riemannian Manifolds
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PublisherThe University of Arizona.
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AbstractA 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.
Degree ProgramGraduate College