Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length

Abstract

We prove that on a compact $n$-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue $\lambda$ of the Dirac operator satisfies the inequality ${\lambda }^2\ge \frac{n-1}{4(n-2)}{\inf }_{M}Scal$. In the limiting case the universal cover of the manifold is isometric to $R\times N$ where $N$ is a manifold admitting Killing spinors.

References in corpus (1)

• The First Dirac Eigenvalue on Manifolds with Positive Scalar Curvature

Cited by in corpus (9)

• Locally conformally Kähler manifolds. A selection of results
• 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
• The mean curvature of transverse Kähler foliations
• Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations
• Lower bounds for the eigenvalue estimates of the submanifold Dirac operator
• The first eigenvalue of the Dirac operator on locally reducible Riemannian manifolds
• The Dirac operator on locally reducible Riemannian manifolds
• Eigenvalue estimate for the Dirac-Witten operator on locally reducible Riemannian manifolds