This page will eventually be a repository of all metrics on 4-manifolds. In time there will be dozens of explicit metrics and explanations of numerous techniques. Currently things are sparse, but with an upload or two per week, the project should be done in no time.
Metrics arranged by type
- Conformal Metrics and Metrics expressed in coordinates
- 4-metrics from frames on the 3-Sphere
- Homogeneity-one metrics
Remark. Not included are metrics that are known to exist but cannot be written down in principle; typically these are metrics whose discovery involves the implicit function theorem and/or a continuity argument. Examples of what is not included are Calabi-Yau metrics, metrics from the Kummer construction such as the Biquard-Minerbe metrics, the Gross-Wilson metrics on K3, and the Chen-Lebrun-Weber metric on CP2#2CP2.
Remark. Sources cited inline.