Realization of Bipartite Weighted Graphs by Stable Gauss Maps
[EN] The singularities of a stable Gauss map of a closed orientable surface immersed generically in three-dimensional Euclidean space, according to H. Whitney¿s Theorem, are of the fold and cusp types. The singular set of a stable Gauss map of a surface, which consists of curves of fold points conta...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/222655 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/222655 |
| Access Level: | acceso abierto |
| Palabra clave: | Stable Gauss maps Bipartite weighted graphs Singularities Parabolic curves Euclidean space |
| Sumario: | [EN] The singularities of a stable Gauss map of a closed orientable surface immersed generically in three-dimensional Euclidean space, according to H. Whitney¿s Theorem, are of the fold and cusp types. The singular set of a stable Gauss map of a surface, which consists of curves of fold points containing isolated cusp points, is the parabolic set on the surface. Each parabolic curve of the singular set separates a hyperbolic region from an elliptic region of the surface. In this work, we will explore how weighted graphs can be associated with stable Gauss maps and present a general result that determines necessary and sufficient conditions for a weighted graph to be associated with a stable Gauss map. |
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