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Article Dans Une Revue Differential Geometry and its Applications Année : 2016

Generic singularities of line fields on 2D manifolds

Résumé

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.
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Dates et versions

hal-01318515 , version 1 (19-05-2016)

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Ugo Boscain, Ludovic Sacchelli, Mario Sigalotti. Generic singularities of line fields on 2D manifolds. Differential Geometry and its Applications, 2016, Volume 49 (December 2016), pp.326-350. ⟨hal-01318515⟩
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