The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature

Abstract

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

7 pages, 3 figures

References in corpus (3)

• 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
• Extrinsic Bounds for Eigenvalues of the Dirac Operator

Cited by in corpus (6)

• 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
• Manifolds with small Dirac eigenvalues are nilmanifolds
• Lower bounds for the eigenvalue estimates of the submanifold Dirac operator
• Eigenvalue estimate for the Dirac-Witten operator on locally reducible Riemannian manifolds
• The Dirac operator on locally reducible Riemannian manifolds