Riemannian Submersions with Discrete Spectrum
| Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
|---|---|
| Data(s) |
29/10/2013
29/10/2013
2012
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| Resumo |
We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products. CNPq-CAPES (Brazil) CNPqCAPES (Brazil) MEC (Spain) MEC (Spain) [PCI2006-A7-0532] |
| Identificador |
JOURNAL OF GEOMETRIC ANALYSIS, NEW YORK, v. 22, n. 2, supl. 1, Part 2, pp. 603-620, APR, 2012 1050-6926 http://www.producao.usp.br/handle/BDPI/36385 10.1007/s12220-010-9207-3 |
| Idioma(s) |
eng |
| Publicador |
SPRINGER NEW YORK |
| Relação |
JOURNAL OF GEOMETRIC ANALYSIS |
| Direitos |
restrictedAccess Copyright SPRINGER |
| Palavras-Chave | #RIEMANNIAN SUBMERSIONS #DISCRETE SPECTRUM #ESSENTIAL SPECTRUM #PURELY CONTINUOUS-SPECTRUM #NEGATIVE CURVATURE #MANIFOLDS #LAPLACIAN #MATHEMATICS |
| Tipo |
article original article publishedVersion |
