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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

## 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 |
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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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