| dc.creator | Eberlein, Patrick | |
| dc.date | 2004-03-01 | |
| dc.date.accessioned | 2019-05-03T12:36:51Z | |
| dc.date.available | 2019-05-03T12:36:51Z | |
| dc.identifier | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1660 | |
| dc.identifier.uri | http://revistaschilenas.uchile.cl/handle/2250/84385 | |
| dc.description | In this article we investigate the geometry of a Lie group N with a left invariant metric, particularly in the case that N is 2-step nilpotent. Our primary interest will be in properties of the geodesic flow, but we describe a more general framework for studying left invariant functions and vector fields on the tangent bundle TN. Here we consider the natural left action λ of N on T N given by λn(ℇ) = (Ln)*(ℇ), where Ln : N ⟶ N denotes left translation by n and (Ln) denotes the differential map of Ln.
For convenience all manifolds in this article are assumed to be connected and C∞ unless otherwise specified. Many of the assertions remain valid true for manifolds that are not connected and are Ck for a small integer k.
We assume that the reader has a familiarity with manifold theory and with the basic concepts of Lie groups and their associated Lie algebras of left invariant vector fields. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/1660/1512 | |
| dc.source | CUBO, A Mathematical Journal; Vol. 6 Núm. 1 (2004): CUBO, A Mathematical Journal; 427–510 | es-ES |
| dc.source | CUBO, A Mathematical Journal; Vol 6 No 1 (2004): CUBO, A Mathematical Journal; 427–510 | en-US |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.title | Left invariant geometry of Lie groups | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
