Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections
In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main re...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1730 |
| _version_ | 1797407778425274368 |
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| author | Jiajing Miao Jinli Yang Jianyun Guan |
| author_facet | Jiajing Miao Jinli Yang Jianyun Guan |
| author_sort | Jiajing Miao |
| collection | DOAJ |
| description | In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>7</mn></msub></semantics></math></inline-formula> do not have Codazzi tensors associated with Yano connections, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>3</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>4</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>5</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>6</mn></msub></semantics></math></inline-formula> have Codazzi tensors associated with Yano connections. |
| first_indexed | 2024-03-09T03:46:35Z |
| format | Article |
| id | doaj.art-8f80094848e5464fa04211d69f863824 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:46:35Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8f80094848e5464fa04211d69f8638242023-12-03T14:33:54ZengMDPI AGSymmetry2073-89942022-08-01148173010.3390/sym14081730Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano ConnectionsJiajing Miao0Jinli Yang1Jianyun Guan2School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, ChinaSchool of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, ChinaSchool of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, ChinaIn this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>7</mn></msub></semantics></math></inline-formula> do not have Codazzi tensors associated with Yano connections, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>3</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>4</mn></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>5</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>6</mn></msub></semantics></math></inline-formula> have Codazzi tensors associated with Yano connections.https://www.mdpi.com/2073-8994/14/8/1730Codazzi tensorsYano connectoinsLorentzian Lie group |
| spellingShingle | Jiajing Miao Jinli Yang Jianyun Guan Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections Symmetry Codazzi tensors Yano connectoins Lorentzian Lie group |
| title | Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections |
| title_full | Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections |
| title_fullStr | Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections |
| title_full_unstemmed | Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections |
| title_short | Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections |
| title_sort | classification of lorentzian lie groups based on codazzi tensors associated with yano connections |
| topic | Codazzi tensors Yano connectoins Lorentzian Lie group |
| url | https://www.mdpi.com/2073-8994/14/8/1730 |
| work_keys_str_mv | AT jiajingmiao classificationoflorentzianliegroupsbasedoncodazzitensorsassociatedwithyanoconnections AT jinliyang classificationoflorentzianliegroupsbasedoncodazzitensorsassociatedwithyanoconnections AT jianyunguan classificationoflorentzianliegroupsbasedoncodazzitensorsassociatedwithyanoconnections |