Classification of quadrics in a double isotropic space

Abstract

This paper gives the classification of second order surfaces in a double isotropic space $I_{3}^{(2)}$. Although quadrics in $I_{3}^{(2)}$ have been investigated earlier [e.g. 8 or 9], this paper offers a new method based on linear algebra. The definition of invariants of a quadric with respect to the group of motions in $I_{3}^{(2)}$ makes it possible to determine the type of a quadric without reducing its equation to a canonical form. For that purpose isometric properties of conics in the isotropic plane and affine properties of quadrics are used