Naslov
Circular Quartics in Pseudo-Euclidean plane

Autori
Jurkin, Ema

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
GeoGra 2012 Conference, Budapest, 20-21/01/2012 / Bolcskei, Attila ; Nagy, Gyula - Budimpešta, 2012

Skup
GeoGra 2012 Conference

Mjesto i datum
Budimpešta, Mađarska, 20.01.2012. - 21.01.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
pseudo-Euclidean plane; type of circularity; quartic; pencil of conics; projectivity

Sažetak
The pseudo-Euclidean plane is a projective plane where the metric is induced by a real line f and two real points F1 and F2 incidental with it. An algebraic curve k of order n intersects the absolute line f in n points. If one of them coincides with one of the absolute points, the curve is said to be circular. If F1 is an intersection point of k and f with the intersection multiplicity r and F2 is an intersection point of k and f with the intersection multiplicity t, then k is said to be a curve with the type of circularity (r, t) and its degree of circularity is defined as r+t. If n=r+t, the curve is entirely circular. A curve of order four in the projective plane can be defined as a locus of the intersection points of pairs of corresponding conics in the projectively linked pencils of conics. We determine the conditions that the pencils of conics and the projectivity have to fulfill in order to obtain a quartic of a certain type. It will be shown that all types of circular quartics in the pseudo-Euclidean plane can be constructed by using this method.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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