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OverviewHigh Quality Content by WIKIPEDIA articles! In mathematics, Mostow's rigidity theorem, sometimes called the strong rigidity theorem, essentially states that the geometry of a finite-volume hyperbolic manifold (for dimension greater than two) is determined by the fundamental group and hence unique. It is the leading example of the types of statements that occur in rigidity theory. While the theorem shows that there is no deformation space of (complete) hyperbolic structures on a finite volume hyperbolic n-manifold (for n > 2), for a hyperbolic surface of genus g > 1 there is a moduli space of dimension 6g 6 that parameterizes all metrics of constant curvature (up to diffeomorphism), a fact essential for Teichmuller theory. In dimension three, there is a non-rigidity theorem due to Thurston called the hyperbolic Dehn surgery theorem; it allows one to deform hyperbolic structures on a finite volume manifold as long as changing homeomorphism type is allowed. In addition, there is a rich theory of deformation spaces of hyperbolic structures on infinite volume manifolds. Full Product DetailsAuthor: Lambert M. Surhone , Mariam T. Tennoe , Susan F. HenssonowPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.40cm , Length: 15.20cm Weight: 0.117kg ISBN: 9786131244476ISBN 10: 6131244472 Pages: 70 Publication Date: 14 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |