A finiteness theorem for the space of harmonic sections

  • Stefano Pigola

    Università dell'Insubria, Como, Italy
  • Marco Rigoli

    Università di Milano, Italy
  • Alberto G. Setti

    Università dell'Insubria, Como, Italy


In this paper we give a unified and improved treatment to finite dimensionality results for subspaces of harmonic sections of Riemannian or Hermitian vector bundles over complete manifolds. The geometric conditions on the manifold are subsumed by the assumption that the Morse index of a related Schr#x00F6;dinger operator is finite. Applications of the finiteness theorem to concrete geometric situations are also presented.

Cite this article

Stefano Pigola, Marco Rigoli, Alberto G. Setti, A finiteness theorem for the space of harmonic sections. Rev. Mat. Iberoam. 24 (2008), no. 1, pp. 91–116

DOI 10.4171/RMI/531