engleski

On Pencil of Quadrics in I_3^(2)

The pencil of quadrics is a set of infinite number of 2nd order surfaces having common 4th order space curve. Intersecting a pencil of quadrics by a general plane we obtain a pencil of 2nd 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. In this process we use the classification of pencils of conics in the isotropic plane, the classification of 2nd order surfaces in I_3^(2), and the projective properties of the pencils of second order surfaces. 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.

quadrics; plane isotropic geometry; geometry of the double isotropic space; pencil of quadrics

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