Two-sided conformally recurrent self-dual spaces

Abstract

Two-sided conformally recurrent 4-dimensional self-dual spaces are considered. It is shown that such spaces are equipped with nonexpanding congruences of null strings. The general structure of weak nonexpanding hyperheavenly spaces is given. Finally, the general metrics of Petrov-Penrose type $[D]x[-]$ spaces are presented.

References in corpus (5)

• Self-Dual Conformal Gravity
• Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four
• On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces
• Conformal and isometric embeddings of gravitational instantons
• One-sided type-D Ricci-flat metrics

Cited by in corpus (1)

• Hyperheavenly spaces and their application in Walker and para-Kähler geometries: Part I