On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces
General Relativity and Quantum Cosmology
2017-11-21 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1610.02498,
title = {On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces},
author = {Adam Chudecki},
journal= {arXiv preprint arXiv:1610.02498},
year = {2017}
}