Classification of quadrics in a double isotropic space

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

Better butterfly theorem in the isotropic plane

A real affine plane A_2 is called an isotropic plane I_2, if in A_2 a metric is induced by an absolute {f, F}, consisting of the line at infinity f of A_2 and a point $Fin f$. Better butterfly theorem is one of the generalisations of the well-known butterfly theorem ([1], [4]). In this paper the better butterfly theorem has been adapted for the isotropic plane and its validity in I_2 has been proved

Metrical relationships in a standard triangle in an isotropic plane

Each allowable triangle of an isotropic plane can be set in a standard position, in which it is possible to prove geometric properties analytically in a simplified and easier way by means of the algebraic theory developed in this paper