Toric, U(2), and LeBrun metrics
Abstract The LeBrun ansatz was designed for scalar-flat Kähler metrics with a continuous symmetry; here we show it is generalizable to much broader classes of metrics with a symmetry. We state the conditions for a metric to be (locally) expressible in LeBrun ansatz form, the conditions under which its natural complex structure is integrable, and the conditions that produce a metric that is Kähler, scalar-flat, or extremal Kähler. Second, toric Kähler metrics (such as the generalized Taub-NUTs) and U(2)-invariant metrics (such as the Fubini-Study or Page metrics) are certainly expressible in the LeBrun ansatz. We give general formulas for such transitions. We close the paper with examples, and find expressions for two examples-the exceptional half-plane metric and the Page metric-in terms of the LeBrun ansatz.
| Main Author: | |
|---|---|
| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2020
|
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462020000300395 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|