Classification of the Killing Vectors in Nonexpanding HH-Spaces with Lambda

TL;DR

This paper classifies Killing vectors in nonexpanding hyperheavenly spaces with a cosmological constant, providing a unified master equation and explicit metric examples, advancing understanding of symmetries in these complex geometries.

Contribution

It introduces a reduction of Killing equations to a single master equation and classifies various types of Killing vectors in these spaces, including new metric examples.

Findings

Reduction of ten Killing equations to one master equation

Classification of homothetic and isometric Killing vectors

Explicit examples of nonexpanding complex metrics

Abstract

Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric Killing vectors in nonexpanding hyperheavenly spaces with Lambda and homothetic Killing vectors in heavenly spaces is given. Some nonexpanding complex metrics of types [III,N]x[N] are found. A simple example of Lorentzian real slice of the type [N]x[N] is explicitly given.