181 citations
- Université Paris CitéFR11 papers
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- Laboratoire de Mathématiques Blaise PascalFR5 papers
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- Universidad Católica del NorteCL2 papers
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5 papers · 1 filter
On geodesic envelopes and caustics
Gianmarco Capitanio
We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the…
Legendrian graphs generated by Tangential Families
Gianmarco Capitanio
We construct a Legendrian version of Envelope theory. A tangential family is a 1-parameter family of rays emanating tangentially from a smooth plane curve. The Legendrian graph of…
Simple tangential families and perestroikas of their envelopes
Gianmarco Capitanio
Tangential families are 1-parameter families of rays emanating tangentially from smooth curves. We classify tangential family germs up to Left-Right equivalence: we prove that ther…
Une Famille De 5-Tissus Plans Exceptionnels
Luc Pirio, Jean-Marie Trépreau
We give a one parameter family of exceptional planar 5-webs. Each web is formed by four pencils of lines and by a foliation defined by the level curves of a function sn_k(x)sn_k(y)…
Stable tangential families and singularities of their envelopes
Gianmarco Capitanio
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 ge…