Helicoidal flat surfaces in the 3-sphere

2016/01/19 by Manfio, Fernando, Santos, João Paulo dos · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.04930

Abstract

In this paper, helicoidal flat surfaces in the 3-dimensional sphere \mathbbS³ 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 \mathbbS³.

Cited by

• Rigidity of Translation Surfaces in the Three-Dimensional Sphere \mathbbS³

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