Canonical Sasakian Metrics
| dc.creator | Boyer, Charles P. | |
| dc.creator | Galicki, Krzysztof | |
| dc.creator | Simanca, Santiago R. | |
| dc.date | 2006-04-13 | |
| dc.date | 2007-03-13 | |
| dc.date.accessioned | 2026-07-07T11:28:13Z | |
| dc.date.available | 2026-07-07T11:28:13Z | |
| dc.description | Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or canonical representatives of the polarization, are Sasakian metrics that are transversally extremal. We define a Sasaki-Futaki invariant of the polarization, and show that it obstructs the existence of constant scalar curvature representatives. For a fixed CR structure of Sasaki type, we define the Sasaki cone of structures compatible with this underlying CR structure, and prove that the set of polarizations in it that admit a canonical representative is open. | |
| dc.description | 36 pages, minor corrections made, example added | |
| dc.identifier | https://arxiv.org/abs/math/0604325 | |
| dc.identifier | http://arxiv.org/abs/math/0604325 | |
| dc.identifier | Commun.Math.Phys.279:705-733,2008 | |
| dc.identifier | doi:10.1007/s00220-008-0429-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/196371 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C25 | |
| dc.title | Canonical Sasakian Metrics | |
| dc.type | text |