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Helicoidal flat surfaces in the 3-sphere

Research paper by Fernando Manfio, João Paulo dos Santos

Indexed on: 19 Jan '16Published on: 19 Jan '16Published in: Mathematics - Differential Geometry



Abstract

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