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PublisherThe University of Arizona.
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AbstractIn this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu.
Degree ProgramGraduate College