We give a necessary and sufficient condition for a non-degenerate symmetric 3-differential with non-zero Blaschke curvature on a complex surface to be locally
representable as a product of three closed holomorphic 1-forms. We give two versions of this condition corresponding to different choices of coordinates, one of which
defines a coordinate-free differential operator, answering a question of Bogomolov
and de Oliveira.

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• Closed symmetric 3-differentials on complex surfaces