Conformally Kähler, Einstein-Maxwell metrics on Hirzebruch surfaces

Abstract

In this note we prove that a special family of Killing potentials on certain Hirzebruch complex surfaces, found by Futaki and Ono, gives rise to new conformally Kähler, Einstein-Maxwell metrics. The correspondent Kähler metrics are ambitoric but they are not given by the Calabi ansatz. This answers in positive questions raised by Futaki-Ono.

22 pages, updated references, corrected typos, revised and expanded section 6, results unchanged. Comments are welcome

References in corpus (3)

• Kähler metrics with constant weighted scalar curvature and weighted K-stability
• The Einstein-Maxwell Equations, Kaehler Metrics, and Hermitian Geometry
• The Einstein-Maxwell Equations and Conformally Kaehler Geometry

Cited by in corpus (1)

• NUTs, Bolts, and Spindles