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Riemannian Submersions with Discrete Spectrum

Bessa, G. Pacelli; Montenegro, J. Fabio; Piccione, Paolo Universidade De São Paulo

JOURNAL OF GEOMETRIC ANALYSIS, NEW YORK, v. 22, n. 2, supl. 1, Part 2, pp. 603-620, APR, 2012

SPRINGER; NEW YORK 2012

Acesso online

  • Título:
    Riemannian Submersions with Discrete Spectrum
  • Autor: Bessa, G. Pacelli; Montenegro, J. Fabio; Piccione, Paolo
  • Universidade De São Paulo
  • Assuntos: Riemannian Submersions; Discrete Spectrum; Essential Spectrum; Purely Continuous-Spectrum; Negative Curvature; Manifolds; Laplacian; Mathematics
  • É parte de: JOURNAL OF GEOMETRIC ANALYSIS, NEW YORK, v. 22, n. 2, supl. 1, Part 2, pp. 603-620, APR, 2012
  • Descrição: 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]
  • DOI: 10.1007/s12220-010-9207-3
  • Títulos relacionados: JOURNAL OF GEOMETRIC ANALYSIS
  • Editor: SPRINGER; NEW YORK
  • Data de publicação: 2012
  • Idioma: Inglês

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