Points singuliers normaux

Jean-Pierre Dax (1)

1 LMAM - Laboratoire de Mathématiques et Applications de Metz

The author studies the singularities of a differential mapping f between differential manifolds with the constraint f(A) included in B where A and B are two differential submanifolds. The author introduces a new notion : that of a normal singular point. In particular he studies some of these points that he calls simple normal singular points. He gives for them an intrinsic definition and a reduced form in local coordinates. The author gives also a model for the elimination of simple normal singular points.

Mots clés: point singulier; singular point; point singulier normal; normal singular point; point singulier normal simple; simple normal singular point; modèle d'élimination; model for the elimination; forme réduite; reduced form; application correcte; application excellente; paire de variétés

Domaines: Topologie générale [math.GN]; Géométrie différentielle [math.DG]; Mathématiques générales [math.GM]

Jean-Pierre Dax. Points singuliers normaux. 2007. ⟨hal-00162276⟩