### On Brocard points in the isotropic plane.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions $d\ge 3$.

We study the measurability of sets of pairs of straight lines with respect to the group of motions in the simply isotropic space $I{\u2083}^{\left(1\right)}$ by solving PDEs. Also some Crofton type formulas are obtained for the corresponding densities.

The measurable sets of pairs of intersecting non-isotropic straight lines of type $\beta $ and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.

**Page 1**