Izvorni znanstveni članak

On pencil of quadrics in I3(2)

Jelena Beban - Brkić ; Geodetski fakultet Sveucilista u Zagrebu, Zavod za geometiku, 10000 Zagreb, Kaciceva 26, Croatia

Sažetak

An affine space A3 is called a double isotropic space I3
(2) , if in A3 a metric is induced by an absolute , f , F, consisting of the line f in the plane of infinity of A3, and a point F in f .
The pencil of quadrics is a set of 1 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 I3
(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 given in 2, the classification of 2nd order surfaces in I3
(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.

Ključne riječi

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

Hrčak ID:

131593

URI

https://hrcak.srce.hr/131593

Datum izdavanja:

1.7.2005.

Posjeta: 671 *