Sasakian structures on CR-manifolds
| dc.creator | Ornea, Liviu | |
| dc.creator | Verbitsky, Misha | |
| dc.date | 2006-06-06 | |
| dc.date | 2006-06-08 | |
| dc.date.accessioned | 2026-07-07T08:38:29Z | |
| dc.date.available | 2026-07-07T08:38:29Z | |
| dc.description | A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of degree 2, $M$ is called Sasakian. A Sasakian manifold is realized naturally as a level set of a Kaehler potential on a complex manifold, hence it is equipped with a pseudoconvex CR-structure. We show that any Sasakian manifold $M$ is CR-diffeomorphic to an $S^1$-bundle of unit vectors in a positive line bundle on a projective Kähler orbifold. This induces an embedding from $M$ to an algebraic cone $C$. We show that this embedding is uniquely defined by the CR-structure. Additionally, we classify the Sasakian metrics on an odd-dimensional sphere equipped with a standard CR-structure. | |
| dc.description | 23 pages, v. 1.1: replaced the abstract, no change in the paper itself | |
| dc.identifier | https://arxiv.org/abs/math/0606136 | |
| dc.identifier | http://arxiv.org/abs/math/0606136 | |
| dc.identifier | Geom. Dedicata 125 (2007), 159--173. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140749 | |
| dc.subject | Differential Geometry | |
| dc.title | Sasakian structures on CR-manifolds | |
| dc.type | text |