Fold singularities on spacelike CMC surfaces in Lorentz-Minkowski space

2015/09/10 by Atsufumi Honda, Honda, Atsufumi, Miyuki Koiso +3
Mathematics · #53C50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Primary 53A10 #Secondary 53A35 #math.DG #msc:53A10 #msc:53A35 #msc:53C50

paper · pdf · doi:10.48550/arxiv.1509.03050

16 pages, 9 figures. Accepted for publication in Hokkaido Mathematical Journal

openalex publication_date 2015/09/10 · arxiv created 2016/02/23 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fold singular points play important roles in the theory of maximal surfaces. For example, if a maximal surface admits fold singular points, it can be extended to a timelike minimal surface analytically. Moreover, there is a duality between conelike singular points and folds. In this paper, we investigate fold singular points on spacelike surfaces with non-zero constant mean curvature (spacelike CMC surfaces). We prove that spacelike CMC surfaces do not admit fold singular points. Moreover, we show that the singular point set of any conjugate CMC surface of a spacelike Delaunay surface with conelike singular points consists of (2,5)-cuspidal edges.

Citations

• Mixed type surfaces with bounded mean curvature in 3-dimensional space-times
• Affine connections and singularities of tangent surfaces to space curves
• Zero mean curvature entire graphs of mixed type in Lorentz-Minkowski 3-space

Related

• Singularities of Maximal Surfaces
• Singularities of spacelike mean curvature one surfaces in de Sitter space
• Singularities of generalized timelike minimal surfaces in Lorentz-Minkowski 3-space
• A Correspondence Between Maximal Surfaces and Timelike Minimal Surfaces in \mathbbL³
• Cuspidal edges and generalized cuspidal edges in the Lorentz-Minkowski 3-space