Eberhard M. Schröder

Zur Kennzeichnung der Lorentz-Transformationen

AbstractLet (V, f) be a real Minkowski space of any, not necessarily finite, dimension, and letd be the corresponding distance function (taking negative values for timelike distances). Then the following statement (among others) is proved: If ϕ :V →V is a surjective mapping such that

Zur Kennzeichnung Fanoscher Affin-Metrischer Geometrien

d(P,Q) = a \Leftrightarrow d(P^\varphi ,Q^\varphi ) = a\forall P,Q \in V

Zur Theorie Subaffiner Inzidenzgruppen

is true for some fixeda εR,a<0, then ϕ is a Lorentz transformation (including a possible translation).

On mappings preserving orthogonality of non-singular vectors

For arbitrary quadratic forms, including the cases of characteristic 2 and of infinite dimensions, several affine-metric and projective-metric structures are considered, and the corresponding isomorphisms are determined. As an application, a general fundamental theorem of the miquelian circle geometry is proved.

Ein einfacher Beweis des Satzes von Alexandroff-Lester

Let V be a vector space over the commutative field K such that char K 2 ∧ 2 ≤ dim V ≤ ∞, and let Q:V → K be a quadratic form of rank ≥ 2. The pair (A(V,K),ξQ), consisting of the affine space A(V,K) and the congruence relation ξQ, defined by (a,b)ξQ (c,d) ⇔ Q(a−b) = Q(c−d) ∀(a,b),(c,d) ∃ V×V, is called an affine-metric fano-space of rank ≥ 2. In this paper, such spaces are characterized by three simple geometrical properties.

On 0-distance-preserving permutations of affine and projective quadrics

AbstractLet (V,K,Q) be a noneuclidean regular metric vector space, ρ a fixed element of K and ϕ: V → V a bijection such that

A 5-Circle Incidence Theorem

Q(x - y) = \rho \leftrightarrow Q(x^\phi - y^\phi ) = \rho \forall x,y \in v.