ON PROJECTIVE UMBILICS: A GEOMETRIC INVARIANT AND AN INDEX
| Affiliation auteurs | Affiliation ok |
| Titre | ON PROJECTIVE UMBILICS: A GEOMETRIC INVARIANT AND AN INDEX |
| Type de publication | Journal Article |
| Year of Publication | 2018 |
| Auteurs | Uribe-Vargas R |
| Journal | JOURNAL OF SINGULARITIES |
| Volume | 17 |
| Pagination | 81-90 |
| Date Published | JAN-DEC |
| Type of Article | Article |
| ISSN | 1949-2006 |
| Mots-clés | cross-ratio, Differential geometry, flecnodal curve, index, Invariant, parabolic curve, projective umbilic, quadratic point, singularity, Surface |
| Résumé | We define a geometric invariant and an index (+1 or -1) for projective umbilics of smooth surfaces. We prove that the sum of the indices of the projective umbilics inside a connected component H of the hyperbolic domain remains constant in any 1-parameter family of surfaces if the topological type of H does not change. We prove the same statement for any connected component E of the elliptic domain. We give formulas for the invariant and for the index which do not depend on any normal form. |
| DOI | 10.5427/jsing.2018.17e |