J. Korean Math. Soc. 2016; 53(6): 1347-1370
Online first article August 25, 2016 Printed November 1, 2016
https://doi.org/10.4134/JKMS.j150524
Copyright © The Korean Mathematical Society.
Eui Chul Kim
Andong National University
On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1 \geq 5, \, m \, \equiv 0 \, \mbox{mod} \, 2,$ we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair $(\varphi_{\frac{m}{2} -1} , \, \varphi_{\frac{m}{2}} )$ of spinor fields (called {\it Sasakian duo}, see Definition 2.1) that solves a special system of two differential equations.
Keywords: Dirac operator, first eigenvalue, Sasakian twistor spinor
MSC numbers: 53C25, 53C27
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