Aleksander Misiak, Eugeniusz Stasiak, Instytut Matematyki, Politechnika Szczecinska, Al. Piastow 17, 70-310 Szczecin, Poland
Abstract: In this note, there are determined all biscalars of a system of $s\leq n$ linearly independent contravariant vectors in $n$-dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation $F(A{\underset1\to u},A {\underset2 \to u},\dots,A{\underset s\to u}) =( \text{sign}( \det A)) F ({\underset1\to u},{\underset2 \to u},\dots,{\underset s\to u}) $ for an arbitrary pseudo-orthogonal matrix $A$ of index one and the given vectors ${\underset1\to u}, {\underset2 \to u},\dots,{\underset s\to u}$.
Keywords: $G$-space, equivariant map, vector, scalar, biscalar
Classification (MSC 2000): 53A55
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