Invariant CR Structures on Compact Homogeneous Manifolds
| dc.creator | Alekseevsky, Dmitry V. | |
| dc.creator | Spiro, Andrea F. | |
| dc.date | 1999-04-13 | |
| dc.date | 2000-12-12 | |
| dc.date.accessioned | 2026-07-07T05:28:40Z | |
| dc.date.available | 2026-07-07T05:28:40Z | |
| dc.description | An explicit classification of simply connected compact homogeneous CR manifolds G/L of codimension one, with non-degenerate Levi form, is given. There are three classes of such manifolds: a) the standard CR homogeneous manifolds which are homogeneous S^1-bundles over a flag manifold F, with CR structure induced by an invariant complex structure on F; b) the Morimoto-Nagano spaces, i.e. sphere bundles $S(N)\subset TN$ of a compact rank one symmetric space N = G/H, with the CR structure induced by the natural complex structure of $TN = G^\C/H^\C$; c) the following manifolds: $SU_n/T^1\cdot SU_{n-2}$, $SU_p\times SU_q/T^1 \cdot U_{p-2}\cdot U_{q-2}$, $SU_n/T^1\cdot SU_2\cdot SU_2\cdot SU_{n-4}$, $SO_{10}/T^1\cdot SO_6$, $E_6/T^1\cdot SO_8$; these manifolds admit canonical holomorphic fibrations over a flag manifold (F,J_F) with typical fiber S(S^k), where k = 2, 3, 5, 7 or 9, respectively; the CR structure is determined by the invariant complex structure J_F on F and by an invariant CR structure on the typical fiber, depending on one complex parameter. | |
| dc.description | In this new version, there are no structural changes from the previous. Some mistakes in the tables of Theorem 1.4, of Theorem 1.5 and of Definition 1.7 have been corrected | |
| dc.identifier | https://arxiv.org/abs/math/9904054 | |
| dc.identifier | http://arxiv.org/abs/math/9904054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78346 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32C16 (Primary); 53C30; 53C15 (Secondary) | |
| dc.title | Invariant CR Structures on Compact Homogeneous Manifolds | |
| dc.type | text |