Complex and CR-structures on compact Lie groups associated to Abelian actions
| dc.creator | Loeb, J. -J. | |
| dc.creator | Manjarin, M. | |
| dc.creator | Nicolau, M. | |
| dc.date | 2006-10-30 | |
| dc.date.accessioned | 2026-07-07T07:29:36Z | |
| dc.date.available | 2026-07-07T07:29:36Z | |
| dc.description | It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently by Charbonnel and Khalgui who have also given a complete algebraic description of these structures. In this article we present an alternative and more geometric construction of this type of invariant structures on a compact Lie group K when it is semisimple. We prove that each left-invariant complex structure, or each CR-structure of maximal dimension with a transverse CR-action by R, is induced by a holomorphic C^l action on a quasi-projective manifold X naturally associated to K. We then show that X admits more general Abelian actions, also inducing complex or CR structures on K which are generically non-invariant. | |
| dc.identifier | https://arxiv.org/abs/math/0610915 | |
| dc.identifier | http://arxiv.org/abs/math/0610915 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118176 | |
| dc.subject | Differential Geometry | |
| dc.subject | 32C10;32C16 | |
| dc.title | Complex and CR-structures on compact Lie groups associated to Abelian actions | |
| dc.type | text |