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 Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 4, Pages 49–63 (Mi faa325)

This article is cited in 11 scientific papers (total in 11 papers)

Special Points of Surfaces in the Three-Dimensional Projective Space

D. A. Panov

Independent University of Moscow

Abstract: In the paper, $3$-jets of two-dimensional surfaces in the three-dimensional affine space are classified. It is shown that there are exactly $22$ types of co-oriented $3$-jets of surfaces. The action of the group of affine transformations on the space of $3$-jets is studied. We calculate a universal complex of singularities that is related to the orbits of the group action. Two linear homology relations for the numbers of special elliptic, hyperbolic, and parabolic points of a compact two-dimensional surface embedded in $\mathbb{R}^3$ are indicated. The stratification of some real cubic surfaces with respect to the types of $3$-jets is described.

DOI: https://doi.org/10.4213/faa325

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English version:
Functional Analysis and Its Applications, 2000, 34:4, 276–287

Bibliographic databases:

UDC: 517
Received: 22.12.1998

Citation: D. A. Panov, “Special Points of Surfaces in the Three-Dimensional Projective Space”, Funktsional. Anal. i Prilozhen., 34:4 (2000), 49–63; Funct. Anal. Appl., 34:4 (2000), 276–287

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Ortiz-Rodriguez, A, “On the special parabolic points and the topology of the parabolic curve of certain smooth surfaces in R-3”, Comptes Rendus Mathematique, 334:6 (2002), 473
2. Ortiz-Rodriguez, A, “Some aspects of the geometry of real algebraic surfaces”, Bulletin Des Sciences Mathematiques, 127:2 (2003), 149
3. R. Uribe-Vargas, “A projective invariant for swallowtails and godrons, and global theorems on the flecnodal curve”, Mosc. Math. J., 6:4 (2006), 731–768
4. Proc. Steklov Inst. Math., 258 (2007), 178–193
5. Hernandez-Martinez L.I. Ortiz-Rodriguez A. Sanchez-Bringas F., “On the Affine Geometry of the Graph of a Real Polynomial”, J. Dyn. Control Syst., 18:4 (2012), 455–465
6. Hernandez Martinez L.I. Ortiz Rodriguez A. Sanchez-Bringas F., “On the Hessian Geometry of a Real Polynomial Hyperbolic Near Infinity”, Adv. Geom., 13:2 (2013), 277–292
7. Sano H. Kabata Y. Silva J.L.D. Ohmoto T., “Classification of Jets of Surfaces in Projective 3-Space Via Central Projection”, Bull. Braz. Math. Soc., 48:4 (2017), 623–639
8. Angel Guadarrama-Garcia M. Ortiz-Rodriguez A., “On the Geometric Structure of Certain Real Algebraic Surfaces”, Geod. Dedic., 191:1 (2017), 153–169
9. Freitas B.R., Garcia R.A., “Inflection Points on Hyperbolic Tori of S-3”, Q. J. Math., 69:2 (2018), 709–728
10. Uribe-Vargas R., “On Projective Umbilics: a Geometric Invariant and An Index”, J. Singul., 17 (2018), 81–90
11. Deolindo Silva J.L. Kabata Yu., “Projective Classification of Jets of Surfaces in 4-Space”, Hiroshima Math. J., 49:1 (2019), 35–46
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