Duality and implicit differential equations

J.W. Bruce, F. Tari

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    We prove some duality results concerning various types of implicit differential equations where F is a smooth function. We show, for instance, that the well folded singularities are self-dual. The results are used to deduce some geometric properties of surfaces in 3-space. So, for example, there are three flecnodal curves at an elliptic flat umbilic and one at a hyperbolic flat umbilic. These curves are tangent to the separatrices of the binary differential equation determining the asymptotic lines.
    Original languageEnglish
    Pages (from-to)791-811
    JournalNonlinearity
    Volume13
    Issue number3
    DOIs
    Publication statusPublished - 2000

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