Original scientific paper

The n-dimensional Simply Isotropic Space

Blaženka Divjak orcid.org/0000-0003-0649-3267 ; Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia

Abstract

Let (In(1), M) be n-dimensional simply isotropic space as it is defined in [3]. The absolute of this Cayley-Klein's geometry consists of the hyperplane ω and the hypersphere Γ of zero radius and Γcω . We shall first determine the group of general isotropic similarities which preserve the absolute. Then we define the isotropic distance d between two points, the isotropic angle φ between two nonisotropic hyperplanes and the isotropic angle ~φ between two isotropic hyperplanes. In case d=0 we shall define the range between points. In case φ=0 (~φ=0) isotropic distance a (isotropic distance φ*)between nonisotropic (isotropic) hyperplanes is defined. All these notions are invariants of the group of isotropic motions which is subgroup of the group of general isotropic similarities. We shall also define distance between a point and a nonisotropic hyperplane. All these invariants for the three dimensional case are given in [2].

Keywords

hyperplane; invariant; isotropic motion; simply isotropic space; transformation

Hrčak ID:

78985

URI

https://hrcak.srce.hr/78985

Publication date:

13.12.1996.

Visits: 1.307 *