Special points of surfaces in a three-dimensional projective space

TY - JOUR

T1 - Special points of surfaces in a three-dimensional projective space

AU - Panov, Dmitri

PY - 2000

Y1 - 2000

N2 - 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 ℝ^3 are indicated. The stratification of some real cubic surfaces with respect to the types of 3-jets is described.

AB - 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 ℝ^3 are indicated. The stratification of some real cubic surfaces with respect to the types of 3-jets is described.

U2 - https://doi.org/10.1023/A:1004157323726

DO - https://doi.org/10.1023/A:1004157323726

M3 - Article

SN - 0016-2663

VL - 34

SP - 276

EP - 287

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

IS - 4

ER -