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In this paper, helicoidal flat surfaces in the $3$-dimensional sphere$\mathbb{S}^3$ are considered. A complete classification of such surfaces isgiven in terms of their first and second fundamental forms and by linearsolutions of the corresponding angle function. The classification is obtainedby using the Bianchi-Spivak construction for flat surfaces and a representationfor constant angle surfaces in $\mathbb{S}^3$.

Helicoidal flat surfaces in the 3-sphere