engleski

Entirely Circular Curves of Order Four in the Hyperbolic Plane Produced by Projective Mapping between two Pencils of Conics

The problem will be studied on the Cayley-Klein's model of the hyperbolic plane. A curve in the hyperbolic plane entirely (completely)circular if it possesses an isotropic asymptote at each intersection point with the absolute. Every curve of order four can be produced by projective mapping between two pencils of conics. The conditions that projective pencils have to fulfill in order to obtain entirely circular quartics of certain type will be determined by using the analytic method. These curves will also be derived in a constructive way.

hyperbolic plane; entirely circular quartic; projective mapping

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