Conformally non-flat Lorentz manifolds and (almost) complex structures

For the problem of incompatibility of complex structures of skies situated along a null geodesic on a generic Lorentz space-time, a workaround is developed, consisting of certain holomorphic linear bundle. We also propose a description of conformally non-flat geometry in terms of an almost CR (Cauchy–Riemann) structure on certain auxiliary bundle. A discussion on application of aforementioned structures beyond Lorentzian geometry is also envisaged.