Complexes in three-dimensional quasi-hyperbolic space 01S3

In the article the canonical frame of a complex is constructed. This frame is geometrically characterized by the fact that in normal correlation the points A0 and A1 (centers of complex-ray) correspond to the planes ( A0 A1 A2) and ( A0 A1A3), which are polar conjugated with respect to the absolute and cross absolute line to the points A2 and A3. The theorem of existence is proved. We have given the geometric characteristics of the complex invariants using three simple ruled surfaces (central surface and two central torses) belonging to the complex. Two main quadratic forms of the complex have been obtained. The ruled surfaces conjugated with respect to the first quadratic form are characterized by the harmonic conjugation of their adherent points. The surfaces conjugated with respect to the second quadratic form are characterized by the harmonic conjugation of the adherent points of one of them with the symmetry points of the other. We have obtained the equation of inflectional centers of the complex generatrices, the conditions characterizing the linear complex, and found some special classes of the complexes.