Harmonic functions, central quadrics, and twistor theory

Abstract

Solutions to the $n$-dimensional Laplace equation which are constant on a central quadric are found. The associated twistor description of the case $n=3$ is used to characterise Gibbons-Hawking metrics with tri-holomorphic $SL(2, \C)$ symmetry.

Final version. To appear in CQG

References in corpus (1)

• Einstein--Weyl spaces and dispersionless Kadomtsev--Petviashvili equation from Painlevé I and II

Cited by in corpus (8)

• On the central quadric ansatz: integrable models and Painleve reductions
• The quadric ansatz for the $mn$-dispersionless KP equation, and supersymmetric Einstein-Weyl spaces
• The large N limit of the Nahm transform
• Supersymmetric black holes with a single axial symmetry in five dimensions
• Gravitational Instantons, Confocal Quadrics and Separability of the Schrödinger and Hamilton-Jacobi equations
• Nahm equations in supersymmetric mechanics
• Magnetic Domains
• Implicit Solutions of PDE's