Generic singularities of line fields on 2D manifolds
| Autor: | Ugo Boscain, Mario Sigalotti, Ludovic Sacchelli |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
010102 general mathematics Conformal map 02 engineering and technology Natural topology Space (mathematics) Umbilical point 01 natural sciences Manifold Computational Theory and Mathematics Principal curvature 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Gravitational singularity Vector field Geometry and Topology 0101 mathematics Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 49:326-350 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2016.09.003 |
| Popis: | Generic singularities of line fields have been studied for lines of principal curvature of embedded surfaces. In this paper we propose an approach to classify generic singularities of general line fields on 2D manifolds. The idea is to identify line fields as bisectors of pairs of vector fields on the manifold, with respect to a given conformal structure. The singularities correspond to the zeros of the vector fields and the genericity is considered with respect to a natural topology in the space of pairs of vector fields. Line fields at generic singularities turn out to be topologically equivalent to the Lemon, Star and Monstar singularities that one finds at umbilical points. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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