Dzyuba V. Disign and transformation of surfaces from conservation of lines of curvature

The dissertation is devoted to disign and transformation of surfaces from conservation of orthogonal webs of coordinate lines and lines of curvature. The sequence of formation of flat orthogonal webs by different modes, their transformation at a surface and the further conformal transformation of the obtained surfaces from conservation of orthogonal webs of coordinate lines and lines of curvature surveyed. Known modes of formation of flat orthogonal webs are supplemented new on the basis of construction of an one-parameter set of curves of a constant both the variable form and searching of orthogonal trajectorieses to them. Transformation of flat orthogonal webs to a surface referred to orthogonal sets of coordinate lines and lines of curvature is founded on known property of projections of a right angle and will consist in the defined distribution of lines of one set on altitude. The further transformation of surfaces is carried out with the help of inversion.