engleski

Curves of the 3rd class obtained by line-inversion in the quasi-hyperbolic plane

The quasi-hyperbolic plane is one of the nine Cayley-Klein projective metrics where the metric is induced by an absolute figure F_QH={;F, f_1, f_2};, consisting of two real lines f_1 and f_2 incidental with the real point F. The line-inversion with respect to a line p and non-degenerated 2nd class curve k is as an involutive quadratic line mapping where the corresponding lines are concurrent with the line p and conjugate with respect to the 2nd class curve k. In this presentation the line-inversion with respect to a circle and different positions of a line will be observed. Furthermore, the notion of circularity for curves will be introduced and types of circular 3rd class curves obtained by line-inversion as images of the 2nd class curves will be analysed.

quasi-hyperbolic plane; line-inversion; circular curve

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