Rigid flat webs on the projective plane

David Marín, Jorge Vitório Pereira

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)


This paper studies global webs on the projective plane with vanishing curvature. The study is based on an interplay of local and global arguments. The main local ingredient is a criterium for the regularity of the curvature at the neighborhood of a generic point of the discriminant. The main global ingredient, the Legendre transform, is an avatar of classical projective duality in the realm of differential equations. We show that the Legendre transform of what we call reduced convex foliations are webs with zero curvature, and we exhibit a countable infinity family of convex foliations which give rise to a family of webs with zero curvature not admitting non-trivial deformations with zero curvature. © 2013 International Press.
Original languageEnglish
Pages (from-to)163-192
JournalAsian Journal of Mathematics
Issue number1
Publication statusPublished - 24 Sep 2013


  • Flat webs
  • Legendre transform
  • Web geometry


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