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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.06706 |
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| _version_ | 1866915469118668800 |
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| author | Blitz, Samuel Silhan, Josef |
| author_facet | Blitz, Samuel Silhan, Josef |
| contents | Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language of higher (Riemannian) fundamental forms. In a similar vein, we also study the geometry of conformal manifolds with embedded hypersurfaces that admits a trivialization of the conformal metric to a product metric, with base manifold given by the embedded hypersurface. We show that the higher conformal fundamental forms play a critical role in their characterization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Fundamental Forms and Warped Product Hypersurfaces Blitz, Samuel Silhan, Josef Differential Geometry Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language of higher (Riemannian) fundamental forms. In a similar vein, we also study the geometry of conformal manifolds with embedded hypersurfaces that admits a trivialization of the conformal metric to a product metric, with base manifold given by the embedded hypersurface. We show that the higher conformal fundamental forms play a critical role in their characterization. |
| title | Higher Fundamental Forms and Warped Product Hypersurfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.06706 |