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

Adam Chudecki

doi:10.1063/1.4994166

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arXiv · 1610.02498

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

Adam Chudecki

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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.

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Adam Chudecki. 2016-10-08. On geometry of congruences of null strings in 4-dimensional complex and real pseudo-Riemannian spaces. https://doi.org/10.1063/1.4994166

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