2016/05/20 by Ugo Boscain, Boscain, Ugo, Ludovic Sacchelli +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG
paper · pdf · doi:10.48550/arxiv.1605.06295
arxiv created 2016/05/20 · openalex publication_date 2016/05/20 · arxiv updated 2016/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.