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.
Eui Chul Kim
Andong National University
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
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