Naslov
Singular Points on Surfaces P_4^6

Autori
Gorjanc, Sonja ; Benić, Vladimir

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

Izvornik
Abstracts of 13th Colloquium on Geometry and Graphics / E. Jurkin, S. Gorjanc - Zagreb : Hrvatsko društvo za geometriju i grafiku, 2008, 6-6

Skup
13th Colloquium on Geometry and Graphics

Mjesto i datum
Poreč, Hrvatska, 07.09.2008. - 11.09.2008

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
quintuple point; quadruple point; tangent cone

Sažetak
The pedal surfaces $\mathcal P_4^6$ with respect to any pole $P$ and one special 1st order 4th class congruence $\mathcal C_4^1$ are 6th order surfaces with a quadruple line. The highest singularity which these surfaces can possess is a quintuple point. The quintuple points on $\mathcal P_4^6$ are classified according to the type of their 5th order tangent cone $-$ six types are obtained. Points on the quadruple line of $\mathcal P_4^6$ are quadriplanar. We distinguish nine types of these points and six of them are the types of pinch-points. Except the singular points on a quadruple line surface $\mathcal P_4^6$ has at least one real double point iff pole $P$ lies on one 5th degree ruled surface (see Fig.~1) and exactly two real double points iff it lies on one parabola.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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