Binary differential equations at parabolic and umbilical points for 2-parameter families of surfaces

J. L. Deolindo-Silva*, Y. Kabata, T. Ohmoto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic 2-parameter families of surfaces in P3 by comparing our projective classification of Monge forms and classification of general BDE obtained by Tari and Oliver. In particular, generic bifurcations of the parabolic curve are classified. The flecnodal curve is also examined by direct computations, and we present new bifurcation diagrams in typical examples.

Original languageEnglish
Pages (from-to)457-473
Number of pages17
JournalTopology and its Applications
Volume234
DOIs
Publication statusPublished - 2018 Feb 1
Externally publishedYes

Keywords

  • Asymptotic curves
  • Binary differential equations
  • Flecnodal curve
  • Parabolic curve
  • Projective differential geometry of surfaces
  • Singularities of smooth maps

ASJC Scopus subject areas

  • Geometry and Topology

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