Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups
Purpose – The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics. Design/methodology/approach – This study aims the classificati...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2024-01-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2022-0010/full/pdf |
| _version_ | 1827375828363640832 |
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| author | Zagane Abdelkader Osamnia Nada Kaddour Zegga |
| author_facet | Zagane Abdelkader Osamnia Nada Kaddour Zegga |
| author_sort | Zagane Abdelkader |
| collection | DOAJ |
| description | Purpose – The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics. Design/methodology/approach – This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively. Findings – This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups. Originality/value – The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric. |
| first_indexed | 2024-03-08T11:58:44Z |
| format | Article |
| id | doaj.art-afade167061f4f3985ac7fad9f352d1f |
| institution | Directory Open Access Journal |
| issn | 1319-5166 2588-9214 |
| language | English |
| last_indexed | 2024-03-08T11:58:44Z |
| publishDate | 2024-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-afade167061f4f3985ac7fad9f352d1f2024-01-23T21:35:57ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142024-01-013019511110.1108/AJMS-01-2022-0010Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groupsZagane Abdelkader0Osamnia Nada1Kaddour Zegga2Department of Mathematics, Faculty of Exact Sciences, Mustapha Stambouli University of Mascara, Mascara, AlgeriaDepartment of Mathematics, Faculty of Exact Sciences, Mustapha Stambouli University of Mascara, Mascara, AlgeriaDepartment of Mathematics, Faculty of Exact Sciences, Mustapha Stambouli University of Mascara, Mascara, AlgeriaPurpose – The purpose of this study is to classify harmonic homomorphisms ϕ : (G, g) → (H, h), where G, H are connected and simply connected three-dimensional unimodular Lie groups and g, h are left-invariant Riemannian metrics. Design/methodology/approach – This study aims the classification up to conjugation by automorphism of Lie groups of harmonic homomorphism, between twodifferent non-abelian connected and simply connected three-dimensional unimodular Lie groups (G, g) and (H, h), where g and h are two left-invariant Riemannian metrics on G and H, respectively. Findings – This study managed to classify some homomorphisms between two different non-abelian connected and simply connected three-dimensional uni-modular Lie groups. Originality/value – The theory of harmonic maps into Lie groups has been extensively studied related homomorphism in compact Lie groups by many mathematicians, harmonic maps into Lie group and harmonics inner automorphisms of compact connected semi-simple Lie groups and intensively study harmonic and biharmonic homomorphisms between Riemannian Lie groups equipped with a left-invariant Riemannian metric.https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2022-0010/full/pdfHarmonic homomorphismsUnimodular Riemannian Lie groupsInvariant metrics |
| spellingShingle | Zagane Abdelkader Osamnia Nada Kaddour Zegga Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups Arab Journal of Mathematical Sciences Harmonic homomorphisms Unimodular Riemannian Lie groups Invariant metrics |
| title | Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups |
| title_full | Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups |
| title_fullStr | Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups |
| title_full_unstemmed | Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups |
| title_short | Classification of harmonic homomorphisms between Riemannian three-dimensional unimodular Lie groups |
| title_sort | classification of harmonic homomorphisms between riemannian three dimensional unimodular lie groups |
| topic | Harmonic homomorphisms Unimodular Riemannian Lie groups Invariant metrics |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-01-2022-0010/full/pdf |
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