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.
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