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Equivariant maps between certain \(G\)-spaces with \(G=O(n-1,1)\). (English) Zbl 1031.53031
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 \({\underset {1} u},{\underset {2} u},\dots ,{\underset {s} u}\).

MSC:
53A55 Differential invariants (local theory), geometric objects
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