On construction of Quadric surfaces from the projective correspondences

Abstract

     Quadric surfaces is surface having many applications in practice, so have many research about it. Have some different ways to construct a Quadric surface. In the book on Projective Geometry (Nguyen Canh Toan, четверухин.ф.1969...), general Quadric surface have constructed basing on the correlation between two bundles of lines and planes, and in the special case it is constructed by the projective correspondences of two bundles of planes.

     In this paper, we introduce the different cases of the correlative correspondences between two bundles of lines and planes to obtain the different forms of Quadric surface. And then we have a general construction for different forms of Quadric surface.