Null Killing vectors and geometry of null strings in Einstein spaces

Abstract

Einstein complex spacetimes admitting null Killing or null homothetic Killing vectors are studied. These vectors define totally null and geodesic 2-surfaces called the null strings or twistor surfaces. Geometric properties of these null strings are discussed. It is shown, that spaces considered are hyperheavenly spaces (HH-spaces) or, if one of the parts of the Weyl tensor vanishes, heavenly spaces (H-spaces). The explicit complex metrics admitting null Killing vectors are found. Some Lorentzian and ultrahyperbolic slices of these metrics are discussed.

References in corpus (1)

• A spinor approach to Walker geometry

Cited by in corpus (4)

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• Summary of session A4: Complex and conformal methods in classical and quantum gravity
• All ASD complex and real 4-dimensional Einstein spaces with $\Lambda \ne 0$ admitting a nonnull Killing vector