Curvature dependent lower bounds for the first eigenvalue of the Dirac operator

Abstract

Using Weitzenböck techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator $D$ and lower bounds for the spectrum of $D^2$ if the curvature satisfies certain conditions.

Latex2e, 14pp

References in corpus (2)

• Eigenvalue estimates for the Dirac operator depending on the Weyl curvature tensor
• A relation between the Ricci tensor and the spectrum of the Dirac operator

Cited by in corpus (2)

• On the spectrum of the twisted Dolbeault Laplacian over Kähler manifolds
• On the eigenvalues of the twisted Dirac operator