Singularities of spacelike mean curvature one surfaces in de Sitter space

2021/03/25 by Honda, Atsufumi, Sato, Himemi
#53A10 #53A35 #53B30 #53C42 #57R45 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.13849

Abstract

In this paper, we study the singularities of spacelike constant mean curvature one (CMC 1) surfaces in the de Sitter 3-space. We prove the duality between generalized conelike singular points and 5/2-cuspidal edges on spacelike CMC 1 surfaces. To describe the duality between A_k+3 singularities and cuspidal S_k singularities, we introduce two invariants, called the α-invariant and σ-invariant, of spacelike CMC 1 surfaces at their singular points. Moreover, we give a classification of non-degenerate singular points on spacelike CMC 1 surfaces.

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