Hypersurfaces of Product Spaces with a Canonical Direction
| Autor: | de Lima, Ronaldo F., Roitman, Pedro |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | Consider a complete Riemannian manifold $M^n$ and let $\Sigma^n$ be an orientable hypersurface of the product manifold $M\times\mathbb{R}$ endowed with its standard product metric $\langle \,,\, \rangle.$ Let $\nabla\xi$ denote the gradient of the height function $\xi$ of $\Sigma.$ In this note, we characterize the hypersurfaces $\Sigma$ which have $\nabla\xi$ as a principal direction. Our approach is based on the work of R. Tojeiro, who considered the case where $M$ is a constant sectional curvature space form. Comment: The results will be included in a different paper |
| Databáze: | arXiv |
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