Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2009; 46(5): 949-966

Printed September 1, 2009

https://doi.org/10.4134/BKMS.2009.46.5.949

Copyright © The Korean Mathematical Society.

Dirac eigenvalues estimates in terms of divergencefree symmetric tensors

Eui Chul Kim

Andong National University

Abstract

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

Keywords: Dirac operator, eigenvalues, divergencefree symmetric tensors

MSC numbers: 53C25, 53C27