Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 125-143.


Jelena Beban-Brkić and Marija Šimić Horvath

Faculty of Geodesy, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: jbeban@geof.hr

Faculty of Architecture, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: marija.simic@arhitekt.hr

Abstract.   This paper gives a complete classification of conics in PE2(R). The classification has been made earlier (Reveruk [5]), but it showed to be incomplete and not possible to cite and use in further studies of properties of conics, pencil of conics, and of quadratic forms in pseudo-Euclidean spaces. This paper provides that. A pseudo-orthogonal matrix, pseudo-Euclidean values of a matrix, diagonalization of a matrix in a pseudo-Euclidean way are introduced. Conics are divided in families and by types, giving both of them geometrical meaning. The invariants of a conic with respect to the group of motions in PE2(R) are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.

2010 Mathematics Subject Classification.   51A05, 51N25.

Key words and phrases.   Pseudo-Euclidean plane PE2(R), conic section.

Full text (PDF) (free access)


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