Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016
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Bull. Korean Math. Soc. 2008; 45(2): 365-373

Printed June 1, 2008

Copyright © The Korean Mathematical Society.

Eigenvalues estimates for the Dirac operator in terms of Codazzi tensors

Thomas Friedrich and Eui Chul Kim

Humboldt-Universit

Abstract

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We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

Keywords: Dirac operator, eigenvalues, Codazzi tensors

MSC numbers: Primary 53C25; Secondary 53C27

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