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On the degeneration of some 3-manifold geometries via unit groups of quaternion algebras

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Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María (2015) On the degeneration of some 3-manifold geometries via unit groups of quaternion algebras. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 109 (2). pp. 669-715. ISSN 1578-7303

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Official URL: http://link.springer.com/article/10.1007/s13398-014-0210-6


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Abstract

A two parameter continuous family of three-dimensional Lie groups with a left invariant Riemannian metric is defined. Each of these Lie groups is the unit group of a quaternion algebra. All the possible left invariant Riemannian structures in the Heisenberg group appear as limit cases. The degeneration of some Thurston’s 3-manifold geometries are studied in this framework. Among other interesting degenerations, the degeneration spherical-Nil-(Formula presented.) is obtained.


Item Type:Article
Uncontrolled Keywords:Quaternion algebra, Lie group, Riemannian geometry
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:33164
Deposited On:17 Sep 2015 08:30
Last Modified:12 Dec 2018 15:12

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