CHARACTERISTIC POINTS, FUNDAMENTAL CUBIC FORM AND EULER CHARACTERISTIC OF PROJECTIVE SURFACES

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TitreCHARACTERISTIC POINTS, FUNDAMENTAL CUBIC FORM AND EULER CHARACTERISTIC OF PROJECTIVE SURFACES
Type de publicationJournal Article
Year of Publication2020
AuteursKazarian M, Uribe-Vargas R
JournalMOSCOW MATHEMATICAL JOURNAL
Volume20
Pagination511-530
Date PublishedJUL-SEP
Type of ArticleArticle
ISSN1609-3321
Mots-cléscusp of Gauss, Differential geometry, flecnodal curve, front, godron, index, parabolic curve, projective umbilic, quadratic point, singularity, Surface
Résumé

We define local indices for projective umbilics and godrons (also called cusps of Gauss) on generic smooth surfaces in projective 3-space. By means of these indices, we provide formulas that relate the algebraic numbers of those characteristic points on a surface (and on domains of the surface) with the Euler characteristic of that surface (resp. of those domains). These relations determine the possible coexistences of projective umbilics and godrons on the surface. Our study is based on a ``fundamental cubic form'', for which we provide a simple expression.
DOI10.17323/1609-4514-2020-20-3-511-530