Deviating congruences of null strings in a certain class of H-spaces of algebraic N type (Q1263106)

H-spaces are 4-dimensional complex manifolds with a complex analytic symmetric covariant non-degenerate (0,2) tensor field \((\ll metric\) \(tensor\gg)\) which satisfy (the complex version of) Einstein vacuum field equations and have the selfdual (resp. antiselfdual) part of their Weyl tensor vanish. The algebraic type N refers to the maximal algebraic specialization (next to vanishing) of the remaining non-zero part (antiselfdual, resp. selfdual) of the Weyl tensor. Null strings are (complex) 2-dimensional surfaces on which the pulled-back metric vanishes; their tangent bivectors must be selfdual or antiselfdual. Congruences of such null strings appear naturally in the study of algebraically special spaces. In this paper, for the type N case, an implicit description of such congruences satisfying a genericity condition is given and is simplified assuming the existence of a Killing vector field. The paper relies heavily on previous work.