Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SASAKIAN TWISTOR SPINORS AND THE FIRST DIRAC EIGENVALUE

  • Kim, Eui Chul (Department of Mathematics College of Education Andong National University)
  • Received : 2015.08.29
  • Published : 2016.11.01
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Abstract

On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1{\geq}5$, $m{\equiv}0$ 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 Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.

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Acknowledgement

Supported by : Andong National University

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