Naslov
Envelopes of the Absolute Quadratic System of Conics of the Hyperbolic Plane I

Autori
Jurkin, Ema ; Roeschel, Otto

Izvornik
Mathematica Pannonica (0865-2090) 19 (2008), 1; 23-35

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Hyperbolic plane; Entirely circular curves of order 4; Quadratic systems of conics; Envelopes of special quadratic systems of conics.

Sažetak
A curve in the hyperbolic plane H2 (we use the Cayley– Kleinmodel) is called entirely (completely) circular if it possesses an isotropic asymptote at each intersection point with the absolute. Any planar curve of fourth order can be generated as an envelope of a quadratic set of conics. If one of these tangent conics coincides with the absolute conic A we refer to it as an absolute quadratic systems of conics. Most of the envelopes of these absolute quadratic systems of conics turn out to be entirely circular. In this paper we characterize absolute quadratic systems of conics which have entirely circular envelopes C4. On such an envelope C4 a triple point may occur. We unambiguously decide which absolute quadratic systems of conics of H2 with absolute conic A deliver triple points of the envelope C4 on A. In a second part of the paper we will give a complete list of types of non-degenerate entirely circular curves of order 4 generated as envelopes of absolute quadratic systems of conics in the hyperbolic plane H2.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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