Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds
| dc.creator | LeBrun, Claude | |
| dc.date | 2004-04-13 | |
| dc.date.accessioned | 2026-07-07T05:07:25Z | |
| dc.date.available | 2026-07-07T05:07:25Z | |
| dc.description | This paper investigates the question of which smooth compact 4-manifolds admit Riemannian metrics that minimize the L2-norm of the curvature tensor. Metrics with this property are called OPTIMAL; Einstein metrics and scalar-flat anti-self-dual metrics provide us with two interesting classes of examples. Using twistor methods, optimal metrics of the second type are constructed on the connected sums kCP_2 for k > 5. However, related constructions also show that large classes of simply connected 4-manifolds do not admit any optimal metrics at all. Interestingly, the difference between existence and non-existence turns out to delicately depend on one's choice of smooth structure; there are smooth 4-manifolds which carry optimal metrics, but which are homeomorphic to infinitely many distinct smooth 4-manifolds on which no optimal metric exists. | |
| dc.description | To appear in "Different Faces of Geometry," Donaldson, Eliashberg, and Gromov, editors; Kluwer/Plenum, 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0404251 | |
| dc.identifier | http://arxiv.org/abs/math/0404251 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70854 | |
| dc.subject | Differential Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 53C20; 53C28; 57R57 | |
| dc.title | Curvature Functionals, Optimal Metrics, and the Differential Topology of 4-Manifolds | |
| dc.type | text |