Singularities of maximal surfaces

By S. Fujimori, Kentaro Saji, Masaaki Umehara, Kotaro Yamada. 2005

157 citations recorded by the source corpus.

We show that the singularities of spacelike maximal surfaces in Lorentz–Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4c1435b3bbfa7ce3cea512b4200727f022890cd5

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In Applied Mathematics

1. Kentaro Saji
2. Masaaki Umehara
3. Kotaro Yamada

In Geometry and Topology

1. Kentaro Saji
2. Masaaki Umehara
3. Kotaro Yamada

Citations in the corpus

• The geometry of fronts (2005, background): “all X∈ TM2. A frontal is a front if (f,ν): M2 → R3×S2 is an immersion. A cuspidal cross cap is a singular point locally diffeomorphic to the map (u,v) → (u,v2,uv3) and is a frontal but not a front. In [FSUY], a useful criterion for cuspidal cross caps are given. Though a cuspidal cross cap is not a c”
• Flat surfaces with singularities in Euclidean 3-space (2006, unknown): “The existence of (U ;u, v) for flat immersion is well-known (See [20] or [3, 5-8]).”