Singularities of improper affine spheres and surfaces of constant Gaussian curvature

By G. Ishikawa, Y. Machida. 2005

71 citations recorded by the source corpus.

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singlarities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvature and for developable surfaces. In particular we confirm that generic singularities appearing in such a surface are just cuspidal edges and awallowtails.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8bcb891bd10cee1a97af63168dfc06120aa6e83c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Kentaro Saji
2. Masaaki Umehara
3. Kotaro Yamada
4. S. Fujimori
5. Satoko Murata

In Geometry and Topology

1. Kentaro Saji
2. Masaaki Umehara
3. Kotaro Yamada
4. S. Fujimori

In Mathematical Physics

1. Kotaro Yamada
2. S. Fujimori
3. Masaaki Umehara
4. Kentaro Saji

Citations in the corpus

• Flat surfaces with singularities in Euclidean 3-space (2006, background): “Finally, we mention several related works: [9] for flat front s in S(3); [26], [4] for behaviour of the Gaussian curvature near cuspidal edges, sw allowtails, and cuspidal cross caps; [30], [16], [3], [17] for singularity of spaceli ke maximal surfaces inR(3)1 and CMC-1 surfaces in de Sitter 3-space”
• Singularities of maximal surfaces (2005, methodology): “It should be also remarked that, analyzing the jet spaces of constant Gaussian curvature surfaces and using the criteria of [KRSUY], Ishikawa-Machida [ IM ] showed generic singularities on surfaces of constant Gaussian curvature in R3 consist of cuspidal”