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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2508.11440 |
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| _version_ | 1866911106223570944 |
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| author | Foka, M. L. Nimpa, R. P. Djiadeu, M. B. N. |
| author_facet | Foka, M. L. Nimpa, R. P. Djiadeu, M. B. N. |
| contents | This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the space of left-invariant vector fields, we derive algebraic characterizations for Killing, one-harmonic Killing, conformal, and concurrent vector fields. Employing a classification of these nilpotent Lie algebras into ten canonical types, we perform a case-by-case analysis to determine the structure of these vector fields. We prove that the space of Killing fields coincides with the center of the Lie algebra, and that one-harmonic and conformal fields are necessarily Killing. Furthermore, we establish the nonexistence of nontrivial concurrent vector fields in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of left-invariant vector fields on Lie groups Foka, M. L. Nimpa, R. P. Djiadeu, M. B. N. Differential Geometry 53C21, 53C23, 53C30 This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the space of left-invariant vector fields, we derive algebraic characterizations for Killing, one-harmonic Killing, conformal, and concurrent vector fields. Employing a classification of these nilpotent Lie algebras into ten canonical types, we perform a case-by-case analysis to determine the structure of these vector fields. We prove that the space of Killing fields coincides with the center of the Lie algebra, and that one-harmonic and conformal fields are necessarily Killing. Furthermore, we establish the nonexistence of nontrivial concurrent vector fields in this setting. |
| title | Geometry of left-invariant vector fields on Lie groups |
| topic | Differential Geometry 53C21, 53C23, 53C30 |
| url | https://arxiv.org/abs/2508.11440 |