The Dirac operator on locally reducible Riemannian manifolds

Abstract

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in the sense that, for the first eigenvalue, they reduce to the result of Alexandrov.

References in corpus (4)

• Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
• Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length
• The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature
• Lower bounds of the Dirac eigenvalues on compact Riemannian spin manifolds with locally product structure