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Legendrian Graphs Generated by Tangential Family Germs

Capitanio, Gianmarco (2006), Legendrian Graphs Generated by Tangential Family Germs, Proceedings of the Edinburgh Mathematical Society, 49, 1, p. 29-37. http://dx.doi.org/10.1017/S0013091504000999

Type
Article accepté pour publication ou publié
External document link
http://arxiv.org/abs/math/0409577v1
Date
2006
Journal name
Proceedings of the Edinburgh Mathematical Society
Volume
49
Number
1
Publisher
Cambridge University Press
Pages
29-37
Publication identifier
Metadata
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Author(s)
Capitanio, Gianmarco
Abstract (EN)
We construct a Legendrian version of envelope theory. A tangential family is a one-parameter family of rays emanating tangentially from a regular plane curve. The Legendrian graph of the family is the union of the Legendrian lifts of the family curves in the projectivized cotangent bundle $PT^*\mathbb{R}^2$. We study the singularities of Legendrian graphs and their stability under small tangential deformations. We also find normal forms of their projections into the plane. This allows us to interpret the beak-to-beak perestroika as the apparent contour of a deformation of the double Whitney umbrella singularity $A_1^\pm$.
Subjects / Keywords
envelope theory; contact geometry; tangential families; Legendrian graphs