Geodesic
Special Points of Surfaces in the Three-Dimensional Projective Space
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 49-63

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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. 
@article{FAA_2000_34_4_a3,
     author = {D. A. Panov},
     title = {Special {Points} of {Surfaces} in the {Three-Dimensional} {Projective} {Space}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {49--63},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a3/}
}
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D. A. Panov. Special Points of Surfaces in the Three-Dimensional Projective Space. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 49-63. http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a3/