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

Lozano Imízcoz, María TeresaMontesinos Amilibia, José María2023-06-182023-06-182015-091578-730310.1007/s13398-014-0210-6https://hdl.handle.net/20.500.14352/24152A 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.engOn the degeneration of some 3-manifold geometries via unit groups of quaternion algebrasjournal articlehttp://link.springer.com/article/10.1007/s13398-014-0210-6http://link.springer.com/restricted access514515.1Quaternion algebraLie groupRiemannian geometryGeometríaTopología1204 Geometría1210 Topología