Conics from the Cartan Decomposition of SO(2,1)

Conics from the Cartan Decomposition of SO(2,1)

The aim of this paper is to introduce and study the class of conics provided by the symmetric matrices of the Cartan decomposition of the Lie group SO(2,1). This class depends on two real parameters as components of the cylinder S1×R and we use a deformation inspired by Finsler indicatrices in order...

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Veröffentlicht in:Mathematics (Basel) 2023-04, Vol.11 (7), p.1580
1. Verfasser: Crasmareanu, Mircea
Format: Artikel
Sprache:eng
Schlagworte:
Cartan decomposition of SO(2,1)
complex variable
conic
Conics
Decomposition
Euclidean space
Lie groups
Mathematical analysis
Mathematics
Matrices (mathematics)
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Zusammenfassung:The aim of this paper is to introduce and study the class of conics provided by the symmetric matrices of the Cartan decomposition of the Lie group SO(2,1). This class depends on two real parameters as components of the cylinder S1×R and we use a deformation inspired by Finsler indicatrices in order to obtain proper ellipses. A complex approach is also included.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11071580