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A projective model of the two-dimensional geometry which is dual to the pseudo-Euclidean geometry. (Croatian. English summary) Zbl 0559.51011

This paper presents a synthetic realization of the two-dimensional geometry which is dual to the pseudo-Euclidean geometry i.e. the HP geometry in the projective plane. In other words, it is a projective model of the geometry which is given. Further, it is demonstrated that all the axioms of the HP geometry, given by G. A. Aleksandrova, are satisfied in this model. Thus, it is proved at the same time that the two-dimensional HP geometry is consistent if the projective plane geometry is so.

MSC:

51M05 Euclidean geometries (general) and generalizations
51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
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