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Sur deux formes équivalentes de la notion de (r,s)-orientation de la géométrie de Klein. (On two equivalent forms of the notion of (r,s)- orientation in the Klein geometry). (French) Zbl 0665.51008
A Klein geometry is a triple (M,G,F), where M is a non-empty set, G is a group and F is an operation assigning to each element of M and each element of G an element of M, such that: (1) \(\forall x\in M \forall g_ 1,g_ 2\in G\) \((F(F(x,g_ 1),g_ 2)=F(x,g_ 2\cdot g_ 1))\), \(\forall x\in M\) \((F(x,e)=x)\), \(\forall x\in M\) \((F(x,g)=x \Rightarrow g=e).\)
For such a geometry the authors give two forms of the so called (r,s)- orientation and prove their equivalence.
Reviewer: V.Dicuonzo

51M99 Real and complex geometry
51M05 Euclidean geometries (general) and generalizations