Schouten like metrics on five dimensional nilpotents Lie groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910970177126400 |
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| author | Foka, Marius Landry Djiadeu, Michel Bertrand Ngaha Bouetou, Thomas Bouetou |
| author_facet | Foka, Marius Landry Djiadeu, Michel Bertrand Ngaha Bouetou, Thomas Bouetou |
| contents | The prescribed Ricci curvature problem involves finding a Riemannian metric g that satisfies the equation ric(g) = T, where T is a fixed symmetric (0, 2)-tensor field on a differential manifold M. In this paper, we introduce the concept of Schouten-like metrics as particular solutions to the prescribed Ricci curvature problem. We classify these metrics on five-dimensional nilpotent Lie groups by establishing a connection with algebraic Schouten solitons. This approach also enables us to classify five-dimensional nilsolitons, providing a comprehensive understanding of their geometric structures and properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schouten like metrics on five dimensional nilpotents Lie groups Foka, Marius Landry Djiadeu, Michel Bertrand Ngaha Bouetou, Thomas Bouetou Differential Geometry 53C20, 53C35, 53C30 The prescribed Ricci curvature problem involves finding a Riemannian metric g that satisfies the equation ric(g) = T, where T is a fixed symmetric (0, 2)-tensor field on a differential manifold M. In this paper, we introduce the concept of Schouten-like metrics as particular solutions to the prescribed Ricci curvature problem. We classify these metrics on five-dimensional nilpotent Lie groups by establishing a connection with algebraic Schouten solitons. This approach also enables us to classify five-dimensional nilsolitons, providing a comprehensive understanding of their geometric structures and properties. |
| title | Schouten like metrics on five dimensional nilpotents Lie groups |
| topic | Differential Geometry 53C20, 53C35, 53C30 |
| url | https://arxiv.org/abs/2412.20000 |