Canonisation reper of complex of lines of theree-dimensional flag

Abstract

The paper studies the three-parameter geometric image of the line - a complex of line of three-dimensional space of the flag. It identifies the main forms that depend linearly on three basic parameters diferentials. The expression of the main correlations that isotropic plane passing through the beam aligns flag center beam. There was a lock, leading to full canonization frame line complex. We obtain the geometric characteristics of the structure of the canonical frame line complex. A condition in which the complex is obtained isotropic complex of lines. Write down the equations of the tangent bundle of linear systems. Obtain basic complex quadratic forms of complex. Also derivation formula obtained canonical frame set of three-dimensional space of the flag. Noted all ruled surfaces, which has a touch of the second order linear isotropic complex.