Classification of Conic Sections in $PE_2(\mathbb{R})$
Metric Geometry
2013-06-18 v1
Abstract
This paper gives a complete classification of conics in . 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 are determined, making it possible to determine a conic without reducing its equation to canonical form. An overview table is given.
Keywords
Cite
@article{arxiv.1306.3817,
title = {Classification of Conic Sections in $PE_2(\mathbb{R})$},
author = {Jelena Beban-Brkić and Marija Šimić Horvath},
journal= {arXiv preprint arXiv:1306.3817},
year = {2013}
}