Circular curves of the 3rd class obtained by projective mapping in QH_2(R)

The metric in QH_2(R) is induced by an absolute fi gure F_QH = (F ; f1 ; f2), consisting of two real lines f1 and f2 incident with the real point F. A curve of class n is circular in the quasi-hyperbolic plane if it contains at least one absolute line. The curves of the 3rd class can be obtained by projective mapping, i.e., obtained by projectively linked pencil of curves of the 2nd class and range of points. The circular curves of the 3rd class of all types, depending on their position to the absolute figure, can be constructed with projectively linked pencils.