Some New Approaches to Rigidity Problems in Riemannian Geometry: Lie Groupoids, Poisson Manifolds and Von Neumann Algebras, Ph.D. Dissertation Sharif University of Technology ; Fanai, Hamid Reza (Supervisor)
Abstract
In this thesis, we study a rigidity problem for a 2-step nilmanifold such as Γ by some information about its geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric, and Γ is a discrete cocompact subgroup of . For the solution to this problem, first, we consider an algebraic aspect of it; since isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, i.e., normalizers. Also, as we will show, proper and smooth actions of Lie groups and closed subgroups of isometries for smooth Riemannian structures can be regarded as the same topic. Then, in a generalized setting, when passing from the case of...
Cataloging briefSome New Approaches to Rigidity Problems in Riemannian Geometry: Lie Groupoids, Poisson Manifolds and Von Neumann Algebras, Ph.D. Dissertation Sharif University of Technology ; Fanai, Hamid Reza (Supervisor)
Abstract
In this thesis, we study a rigidity problem for a 2-step nilmanifold such as Γ by some information about its geodesic flows, where is a simply connected 2-step nilpotent Lie group with a left invariant metric, and Γ is a discrete cocompact subgroup of . For the solution to this problem, first, we consider an algebraic aspect of it; since isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, i.e., normalizers. Also, as we will show, proper and smooth actions of Lie groups and closed subgroups of isometries for smooth Riemannian structures can be regarded as the same topic. Then, in a generalized setting, when passing from the case of...
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