On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces

Abstract

4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which are called the null strings. Properties of congruences (foliations) of such 2-surfaces are studied. Some relations between properties of congruences of null strings, Petrov-Penrose type of SD Weyl spinor and algebraic types of the traceless Ricci tensor are analyzed.

References in corpus (3)

• A Goldberg-Sachs theorem in dimension three
• On some examples of para-Hermite and para-Kähler Einstein spaces with $\Lambda \ne 0$
• Classification of the traceless Ricci tensor in 4-dimensional pseudo-Riemannian spaces of neutral signature

Cited by in corpus (5)

• Hyperheavenly spaces and their application in Walker and para-Kähler geometries: Part I
• Two-sided conformally recurrent self-dual spaces
• On twisting type $[\text{N}]\otimes [\text{N}]$ Ricci flat complex spacetimes with two homothetic symmetries
• Hyperheavenly spaces and their application in Walker and para-Kähler geometries: part II
• On Walker and para-Hermite Einstein spaces