Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary
| Autor: | Chami, Fida El, Habib, Georges, Makhoul, Ola, Nakad, Roger |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic $1$-forms defined on a compact manifold whose boundary is endowed with a Riemannian flow. The limiting case gives rise to a particular geometry of the flow and the boundary. Namely, the flow is a local product and the boundary is $\eta$-umbilical. This allows to characterize the quotient of $\mathbb R\times B'$ by some group $\Gamma$ as being the limiting manifold. Here $B'$ denotes the unit closed ball. Finally, we deduce several rigidity results describing the product $\mathbb{S}^1\times \mathbb{S}^n$ as the boundary of a manifold. Comment: 16 pages |
| Databáze: | arXiv |
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