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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.19177 |
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| _version_ | 1866929743438282752 |
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| author | Cardoso, Isolda Cosgaya, Ana Reggiani, Silvio |
| author_facet | Cardoso, Isolda Cosgaya, Ana Reggiani, Silvio |
| contents | A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for $6$-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds Cardoso, Isolda Cosgaya, Ana Reggiani, Silvio Differential Geometry 53C30, 22E25 A real Lie algebra is said to be characteristically solvable if its derivation algebra is solvable. We explicitly determine the moduli space of left-invariant metrics, up to isometric automorphism, for $6$-dimensional nilmanifolds whose associated Lie algebra is characteristically solvable of triangular type. We also compute the corresponding full isometry groups. For each left-invariant metric on these nilmanifolds we compute the index and distribution of symmetry. In particular, we find the first known examples of Lie groups which do not admit a left-invariant metric with positive index of symmetry. As an application we study the index of symmetry of nilsoliton metrics. We prove that nilsoliton metrics detect the existence of left-invariant metrics with positive index of symmetry. |
| title | The moduli space of left-invariant metrics on six-dimensional characteristically solvable nilmanifolds |
| topic | Differential Geometry 53C30, 22E25 |
| url | https://arxiv.org/abs/2404.19177 |