an:01682571
Zbl 1031.53031
Misiak, Aleksander; Stasiak, Eugeniusz
Equivariant maps between certain \(G\)-spaces with~\(G=O(n-1,1)\)
EN
Math. Bohem. 126, No. 3, 555-560 (2001).
00081881
2001
j
53A55
\(G\)-space; equivariant map; vector; scalar; biscalar
Summary: The authors determine 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 \(F(A{\underset {1} u},A{\underset {2} u},\dots ,A{\underset {s} u}) =(\text{sign}(\det A)) F({\underset {1} u},{\underset {2} u},\dots ,{\underset {s} u}) \) for an arbitrary pseudo-orthogonal matrix \(A\) of index one and the given vectors \({\underset {1} u},{\underset {2} u},\dots ,{\underset {s} u}\).