Orthogonalitätsrelationen mit Parallelinvarianz und Zentralbündel von Schrägspiegelungen an Ebenen im äquiaffinen Raum. (On orthogonality relations with invariance of parallelity and central bundles of skew reflections on planes in equi-affine spaces)
In a 3-dimensional affine space over a commutative field of characteristic \(\neq 2\) the authors study orthogonality relations between lines and planes with the following properties: Compatibility with \(\|\); a richness condition; two spatial generalizations of the statement, that the altitudes of a triangle intersect in a common point. A description of these orthogonality relations is given in terms of linear algebras. Furthermore, the authors study relations between skew reflections which have a plane E as axis and the parallel class of perpendiculars to E for center.
scientific article; zbMATH DE number 4129527