Let D be a division ring with an involution and F = {a ∈ D | a = a}. When is the identity map then D = F is a field and we assume char(F ) = 2. When is not the identity map we assume that F is a subfield of D and is contained in the center of D. Let n be an integer, n ≥ 2, and Hn(D) be the space of hermitian matrices which includes the space Sn(F ) of symmetric matrices as a particular case. If a bijective map ϕ of Hn(D) preserves the adjacency then also ϕ −1 preserves the adjacency. Mathematics Subject Classification (2000). 15A99, 51D20.

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Abstract. Let n ≥ 2 be an integer and let D be a domain of R n . Let f : D → R n be an injective mapping which takes hyperspheres whose interior is contained in D to hyperspheres in R n . Then f is the restriction of a Möbius transformation.

A metric line of the real distance space (S, δ) is the image of an isometric mapping of the Euclidean line R to S. We determine all metric lines of Lorentz-Minkowski geometry. (2000). 51M25, 39B22, 46B20, 05D10. Mathematics Subject Classification

There are no periodic lines in Lorentz-Minkowski geometry. Mathematics Subject Classification (2000). 51M25, 39B22, 46B20.