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This article is cited in 1 scientific paper (total in 1 paper)
Characteristic points, fundamental cubic form and Euler characteristic of projective surfaces
Maxim Kazarianab, Ricardo Uribe-Vargascd a National Research University Higher School of Economics, Moscow, Russia
b Skolkovo Institute of Science and Technology, Moscow, Russia
c Laboratory Solomon Lefschetz UMI2001 CNRS, Universidad Nacional Autonoma de México, México City
d Institut de Mathématiques de Bourgogne, UMR 5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France
Abstract:
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.
Key words and phrases:
differential geometry, surface, front, singularity, parabolic curve, flecnodal curve, index, projective umbilic, quadratic point, godron, cusp of Gauss.
Citation:
Maxim Kazarian, Ricardo Uribe-Vargas, “Characteristic points, fundamental cubic form and Euler characteristic of projective surfaces”, Mosc. Math. J., 20:3 (2020), 511–530
Linking options:
https://www.mathnet.ru/eng/mmj776 https://www.mathnet.ru/eng/mmj/v20/i3/p511
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Abstract page: | 150 | References: | 21 |
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