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http://dx.doi.org/10.4134/JKMS.2005.42.6.1169

THE PROPERTIES OF THE TRANSVERSAL KILLING SPINOR AND TRANSVERSAL TWISTOR SPINOR FOR RIEMANNIAN FOLIATIONS  

Jung, Seoung-Dal (Department of Mathematics Dheju National University)
Moon, Yeong-Bong (Department of Mathematics Dheju National University)
Publication Information
Journal of the Korean Mathematical Society / v.42, no.6, 2005 , pp. 1169-1186 More about this Journal
Abstract
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;
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1 J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194   DOI
2 H. Baum, T. Friedrich, R. Grunewald, and I. Kath, Twistor and Killing Spinors on Riemannian Manifolds, Seminarbericht Nr. 108, Humboldt-Universitat zu Berlin, 1990
3 J. Bruning and F. W. Kamber, Vanishing theorems and index formulas for transversal Dirac operators, A.M.S Meeting 845, Special Session on operator theory and applications to Geometry, Lawrence, KA; A.M.S. Abstracts, Octo- ber, 1988
4 D. Dominguez, A tenseness theorem for Riemannian foliations, C. R. Acad.Sci. Ser. I 320 (1995), 1331-1335
5 T. Friedrich, On the conformal relation between twistors and Killing spinors, Suppl. Rend. Circ. Mat. Palermo (1989), 59-75
6 J. S. Pak and S. D. Jung, A transversal Dirac operator and some vanishing theoerems on a complete foliated Riemannian manifold, Math. J. Toyama Univ. 16 (1993), 97-108
7 S. D. Jung, B. H. Kim, and J. S. Pak, Lower bounds for the eigenvalues of the basic Dirac operator on a Riemannian foliation, J. Geom. Phys. 51 (2004), 166-182   DOI   ScienceOn
8 F. W. Kamber and Ph. Tondeur, Harmonic foliations, Proc. National Science Foundation Conference on Harmonic Maps, Tulane, Dec. 1980, Lecture Notes in Math. 949, Springer-Verlag, New York, 1982, 87-121
9 H. B. Lawson, Jr. and M. L. Michelsohn, Spin geometry, Princeton Univ. Press, Princeton, New Jersey, 1989
10 P. March, M. Min-Oo, and E. A. Ruh, Mean curvature of Riemannian foliations, Canad. Math. Bull. 39 (1996), 95-105   DOI
11 A. Mason, An application of stochastic flows to Riemannian foliations, Houston J. Math. 26 (2000), 481-515
12 E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), 1249-1275   DOI
13 R. Penrose and W. Rindler, Spinors and Space Time, Cambr. Mono. in Math. Physics, 2 (1986)
14 J. F. Glazebrook and F. W. Kamber, Transversal Dirac families in Riemannian foliations, Comm. Math. Phys. 140 (1991), 217-240   DOI
15 K. Habermann, Twistor spinors and their zeros, J. Geom. Phys. 14 (1994), 1-24   DOI   ScienceOn
16 J. J. Hebda, Curvature and focal points in Riemannian foliation, Indiana Univ. Math. J. 35 (1986), 321-331
17 S. D. Jung, The first eigenvalue of the transversal Dirac operator, J. Geom. Phys. 39 (2001), 253-264   DOI   ScienceOn
18 S. D. Jung, Basic Dirac operator and transversal twister operator,, Proceedings of the Eighth International Workshop on Differential Geometry 8 (2004), 157-169
19 Ph. Tondeur, Foliations on Riemannian manifolds, Springer-Verlag, New-York, 1988
20 A. Lichnerowicz, On the twistor-spinors, Lett. Math. Phys. 18 (1989), 333-345   DOI