Lie Ball as Tangent Space to Poincare Space
| dc.creator | Tambekou, Roger Tchangang | |
| dc.date | 2006-12-06 | |
| dc.date.accessioned | 2026-07-07T07:34:41Z | |
| dc.date.available | 2026-07-07T07:34:41Z | |
| dc.description | We equip the whole tangent space $TM$ to a hyperbolic manifold $M$ (of constant sectional curvature -1) with a natural metric in an intrinsic way, so that the isometries of $M$ extend to isometries of $TM$ by holomorphic continuation. The image to the tangent space to a geodesic is equivalent to a hyperbolic disk. In the case of hyperbolic space, we exhibit an equivariant diffeomorphism between $TM$ and the fourth symmetric complex domain of E. Cartan, also known as the Lie ball. The closure of the Lie ball appears as a horospheric compactification of the tangent bundle to hyperbolic space, and its Bergmann metric gives an intrinsic natural kähler metric on the tangent space $TM$. The equivariant map has a simple geometric interpretation. | |
| dc.identifier | https://arxiv.org/abs/math/0612155 | |
| dc.identifier | http://arxiv.org/abs/math/0612155 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119854 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 51M10, 58A05 | |
| dc.title | Lie Ball as Tangent Space to Poincare Space | |
| dc.type | text |