Killing Symmetries in $\mathcal{H}$-Spaces with $\Lambda$

Abstract

All Killing symmetries in complex $\mathcal{H}$-spaces with $\Lambda$ in terms of the Plebański - Robinson - Finley coordinate system are found. All $\mathcal{H}$-metrics with $\Lambda$ admitting a null Killing vector are explicitly given. It is shown that the problem of non-null Killing vector reduces to looking for solution of the Boyer - Finley - Plebański (Toda field) equation

References in corpus (1)

• A Note on Riemannian Anti-self-dual Einstein metrics with Symmetry

Cited by in corpus (5)

• On the Einstein-Weyl and conformal self-duality equations
• Self-Dual Conformal Gravity
• Null Killing vectors and geometry of null strings in Einstein spaces
• Proper conformal symmetries in SD Einstein spaces
• All ASD complex and real 4-dimensional Einstein spaces with $\Lambda \ne 0$ admitting a nonnull Killing vector