2013/06/17 by Jelena Beban-Brkić, Beban-Brkić, Jelena, Marija Šimić Horvath +1
Mathematics · #51A05 #51N25 #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #math.MG #msc:51A05 #msc:51N25
paper · pdf · doi:10.48550/arxiv.1306.3817
arxiv created 2013/06/17 · openalex publication_date 2013/06/17 · arxiv updated 2013/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.