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Eigenvalues of the Laplacian and extrinsic geometry

Hassannezhad, Asma

In: Annals of Global Analysis and Geometry, 2013, vol. 44, no. 4, p. 517-527

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    Titel
    • Eigenvalues of the Laplacian and extrinsic geometry
    Autor
    • Hassannezhad, Asma. Université de Neuchâtel, Institut de Mathématiques, Rue Emile-Argand 11, Case postale 158, 2009, Neuchâtel, Switzerland
    Dokumententyp
    • Postprint
    Sprache
    • Englisch
    Veröffentlicht in
    • Annals of Global Analysis and Geometry, 2013, vol. 44, no. 4, p. 517-527. Springer Netherlands
    Andere elektronische Ausgabe
    OAI-PMH-ID
    • oai:doc.rero.ch:310111
    Summary
    We extend the results given by Colbois, Dryden and El Soufi on the relationships between the eigenvalues of the Laplacian and an extrinsic invariant called intersection index, in two directions. First, we replace this intersection index by invariants of the same nature which are stable under small perturbations. Second, we consider complex submanifolds of the complex projective space $$\mathbb C P^N$$ C P N instead of submanifolds of $$\mathbb R ^N$$ R N and we obtain an eigenvalue upper bound depending only on the dimension of the submanifold which is sharp for the first non-zero eigenvalue