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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
##### Keywords:
$$G$$-space; equivariant map; vector; scalar; biscalar
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