Stable tangential families and singularities of their envelopes

Gianmarco Capitanio (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study tangential families, i.e. systems of rays emanating tangentially from given curves. We classify, up to Left-Right equivalence, stable singularities of tangential family germs (under deformations among tangential families) and we study their envelopes. We discuss applications of our results to the case of tangent geodesics of a curve.

Mots clés: Tangential families; Envelope theory; Singularity Theory; L-R equivalence; Tangential families.

Domaines: Géométrie différentielle [math.DG]

Gianmarco Capitanio. Stable tangential families and singularities of their envelopes. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2005, 341 (8), pp.503--508. ⟨hal-00002154v2⟩