Conics from the Cartan Decomposition of <i>SO</i>(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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/7/1580 |
| _version_ | 1827746736294068224 |
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| author | Mircea Crasmareanu |
| author_facet | Mircea Crasmareanu |
| author_sort | Mircea Crasmareanu |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. This class depends on two real parameters as components of the cylinder <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>S</mi><mn>1</mn></msup><mo>×</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula> and we use a deformation inspired by Finsler indicatrices in order to obtain proper ellipses. A complex approach is also included. |
| first_indexed | 2024-03-11T05:30:32Z |
| format | Article |
| id | doaj.art-41ce330a9bca48f9a6f5e80c1adc346d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:32Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-41ce330a9bca48f9a6f5e80c1adc346d2023-11-17T17:07:39ZengMDPI AGMathematics2227-73902023-03-01117158010.3390/math11071580Conics from the Cartan Decomposition of <i>SO</i>(2,1)Mircea Crasmareanu0Faculty of Mathematics, University “Alexandru Ioan Cuza”, 700506 Iasi, RomaniaThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>O</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. This class depends on two real parameters as components of the cylinder <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>S</mi><mn>1</mn></msup><mo>×</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula> and we use a deformation inspired by Finsler indicatrices in order to obtain proper ellipses. A complex approach is also included.https://www.mdpi.com/2227-7390/11/7/1580conicCartan decomposition of <i>SO</i>(2,1)complex variable |
| spellingShingle | Mircea Crasmareanu Conics from the Cartan Decomposition of <i>SO</i>(2,1) Mathematics conic Cartan decomposition of <i>SO</i>(2,1) complex variable |
| title | Conics from the Cartan Decomposition of <i>SO</i>(2,1) |
| title_full | Conics from the Cartan Decomposition of <i>SO</i>(2,1) |
| title_fullStr | Conics from the Cartan Decomposition of <i>SO</i>(2,1) |
| title_full_unstemmed | Conics from the Cartan Decomposition of <i>SO</i>(2,1) |
| title_short | Conics from the Cartan Decomposition of <i>SO</i>(2,1) |
| title_sort | conics from the cartan decomposition of i so i 2 1 |
| topic | conic Cartan decomposition of <i>SO</i>(2,1) complex variable |
| url | https://www.mdpi.com/2227-7390/11/7/1580 |
| work_keys_str_mv | AT mirceacrasmareanu conicsfromthecartandecompositionofisoi21 |