Flat 3-manifolds with diagonal metrics and applications to warped products
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917101641400320 |
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| author | Blaga, Adara M. Latcu, Dan Radu |
| author_facet | Blaga, Adara M. Latcu, Dan Radu |
| contents | We provide necessary and sufficient conditions for a $3$-dimensional submanifold of $\mathbb R^3$ endowed with a diagonal metric to be flat. As applications, we characterize the flat manifolds of warped product-type, more precisely, the warped, biwarped, sequential warped, and doubly warped product manifolds, and we state the corresponding nonexistence results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flat 3-manifolds with diagonal metrics and applications to warped products Blaga, Adara M. Latcu, Dan Radu Differential Geometry We provide necessary and sufficient conditions for a $3$-dimensional submanifold of $\mathbb R^3$ endowed with a diagonal metric to be flat. As applications, we characterize the flat manifolds of warped product-type, more precisely, the warped, biwarped, sequential warped, and doubly warped product manifolds, and we state the corresponding nonexistence results. |
| title | Flat 3-manifolds with diagonal metrics and applications to warped products |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2502.03064 |