On rotating plane-fronted waves and their Poincaré-invariant differential geometry

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Abstract
After reviewing the rotating plane‐fronted wave type solutions of the scalar wave equation and Maxwell’s vacuum equations in flat space (we point out that there are Yang–Mill analogs as well), we study their Poincaré‐invariant geometry by discussing their characteristic differential invariants and a noninertial curvilinear coordinate system canonically associated with them. In one of the appendices we treat the shearfree and the nondiverging null hypersurfaces in complex Minkowski space, in another one we derive the Yang–Mills version of Robinson’s theorem on null electromagnetic fields.

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