Abstract
Starting from Friedlander's finding that real scalar waves of the simply-progressive type in Minkowski space may reside only on null hypersurfaces constructed from Dupin cyclides, or degenerations thereof, the case of complex-valued wave functions is investigated, assuming (local) analyticity. It is found that they can reside not only on the complex versions of Friedlander's hypersurfaces in complex Minkowski space but also on null hypersurfaces constructed from Monge surfaces. These are also described in twistor terms. The investigation is purely local.
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