Note on the spectrum of the Hodge-Laplacian for k-forms on minimal Legendre submanifolds in \(S^{2n+1}\)

  • Knut Smoczyk
Original article


Given a minimal Legendre immersion L in \(S^{2n+1}\) and \(n\ge k\ge 1\) we prove that \(n+1-k\) is an eigenvalue of the Hodge-Laplacian acting on k and (k-1)-forms on L. In particular we show that the eigenspaces Eig\(_k(n+1-k)\) and Eig\(_{k-1}(n+1-k)\) are at least of dimension \(\left(\begin{array} c{n}{k}\end{array}\right)\)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Knut Smoczyk
    • 1
  1. 1.Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, GermanyDE

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