Dirac eigenvalues estimates in terms of divergencefree symmetric tensors
Bull. Korean Math. Soc. 2009 Vol. 46, No. 5, 949-966
https://doi.org/10.4134/BKMS.2009.46.5.949
Printed September 1, 2009
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
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