On Pencil of Quadrics in I_3^(2)

An affine space A 3 is called a double isotropic space I 3 2 ( ) , if in A 3 a metric is induced by an absolute {w, f , F}, consisting of the line f in the plane of infinity w of A 3 , and a point F Î f .The pencil of quadrics is a set of ¥ 1 2 nd order surfaces having common 4 th order space curve.Intersecting a pencil of quadrics by a general plane we obtain a pencil of 2 nd order curves.In this paper pencils of quadrics in a double isotropic space I 3 2 ( ) are analysed whereby the pencil of surfaces is observed as the pencil associated with the pencil of second order curves (conics) belonging to isotropic absolute plane w.In this process we use the classification of pencils of conics in the isotropic plane given in [2], the classification of 2 nd order surfaces in I 3 2 ( ) [4], and the projective properties of the pencils of second order surfaces [9,16].In order to obtain a more complete classification, the fundamental curve of the pencil, the curve of the centres, and the focal surface of the pencil of quadrics are analysed.