Generic singularities of line fields on 2D manifolds

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 t...

Full description

Saved in:
Bibliographic Details
Published in:Differential geometry and its applications 2016-12, Vol.49 (December 2016), p.326-350
Main Authors: Boscain, Ugo, Sacchelli, Ludovic, Sigalotti, Mario
Format: Article
Language:English
Subjects:
Differential Geometry
Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0926-2245
1872-6984
DOI:10.1016/j.difgeo.2016.09.003