The gap of the eigenvalues for p-forms and harmonic p-forms of constant length

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Abstract

We study the k th positive eigenvalue λk(p) (M, g) of the Laplacian on p-forms for a connected oriented closed Riemannian manifold (M, g). If all non-trivial harmonic p-forms on (M, g) have constant length, then it follows that λk(p) (M, g) ≤ λk(0) (M, g) for all k ≥ 1.

Original languageEnglish
Pages (from-to)476-484
Number of pages9
JournalJournal of Geometry and Physics
Volume54
Issue number4
DOIs
Publication statusPublished - 2005 Aug

Keywords

  • Eigenvalue
  • Gap
  • Harmonic forms of constant length
  • Laplacian on forms

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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