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J. Korean Math. Soc. 2005; 42(6): 1169-1186

Printed November 1, 2005

Copyright © The Korean Mathematical Society.

The properties of the transversal Killing spinor and transversal twistor spinor for Riemannian foliations

Seoung Dal Jung and Yeong Bong Moon

Cheju National University, Cheju National University

Abstract

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We study the properties of the transversal Killing and twistor spinors for a Riemannian foliation with a transverse spin structure. And we investigate the relations between them. As an application, we give a new lower bound for the eigenvalues of the basic Dirac operator by using the transversal twistor operator.

Keywords: transversal Dirac operator, transversal Killing spinor, transversal twistor spinor

MSC numbers: 53C12, 53C27, 57R30

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