Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 498

Eigenvalue estimates of the Dirac operator depending on the Ricci tensor

Thomas Friedrich, Klaus-Dieter Kirchberg

We prove a new lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold by refined Weitzenb"ock techniques. It applies to manifolds with harmonic curvature tensor and depends on the Ricci tensor. Examples show how it behaves compared to other known bounds.

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