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 R3 are indicated. The stratification of some real cubic surfaces with respect to the types of 3-jets is described.
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
\Bibitem{Pan00}
\by D.~A.~Panov
\paper Special Points of Surfaces in the Three-Dimensional Projective Space
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 4
\pages 49--63
\mathnet{http://mi.mathnet.ru/faa325}
\crossref{https://doi.org/10.4213/faa325}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1818284}
\zmath{https://zbmath.org/?q=an:0980.58002}
\elib{https://elibrary.ru/item.asp?id=5021301}
\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 4
\pages 276--287
\crossref{https://doi.org/10.1023/A:1004157323726}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000166603100004}
Linking options:
https://www.mathnet.ru/eng/faa325
https://doi.org/10.4213/faa325
https://www.mathnet.ru/eng/faa/v34/i4/p49
This publication is cited in the following 13 articles:
D. Dreibelbis, W. Olsen, “Structure and transitions of line bitangencies in a family of surface pairs”, J. Geom., 113:2 (2022)
Maxim Kazarian, Ricardo Uribe-Vargas, “Characteristic points, fundamental cubic form and Euler characteristic of projective surfaces”, Mosc. Math. J., 20:3 (2020), 511–530
Deolindo Silva J.L. Kabata Yu., “Projective Classification of Jets of Surfaces in 4-Space”, Hiroshima Math. J., 49:1 (2019), 35–46
Freitas B.R., Garcia R.A., “Inflection Points on Hyperbolic Tori of S-3”, Q. J. Math., 69:2 (2018), 709–728
Uribe-Vargas R., “On Projective Umbilics: a Geometric Invariant and An Index”, J. Singul., 17 (2018), 81–90
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
Angel Guadarrama-Garcia M. Ortiz-Rodriguez A., “On the Geometric Structure of Certain Real Algebraic Surfaces”, Geod. Dedic., 191:1 (2017), 153–169
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
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
Proc. Steklov Inst. Math., 258 (2007), 178–193
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
Ortiz-Rodriguez, A, “Some aspects of the geometry of real algebraic surfaces”, Bulletin Des Sciences Mathematiques, 127:2 (2003), 149
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
Citation in format AMSBIB
Contact us: