MATHEMATICA BOHEMICA, Vol. 126, No. 3, pp. 555-560 (2001)

Equivariant maps between certain $G$-spaces with $G=O( n-1,1)$.

Aleksander Misiak, Eugeniusz Stasiak

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{\underset 1\to u},A {\underset 2 \to u},\dots ,A{\underset s\to u}) =( \text {sign}( \det A)) F ({\underset 1\to u},{\underset 2 \to u},\dots ,{\underset s\to u}) $ for an arbitrary pseudo-orthogonal matrix $A$ of index one and the given vectors ${\underset 1\to u}, {\underset 2 \to u},\dots ,{\underset s\to u}$.

Keywords: $G$-space, equivariant map, vector, scalar, biscalar

Classification (MSC2000): 53A55

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