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THE PROPERTIES OF THE TRANSVERSAL KILLING SPINOR AND TRANSVERSAL TWISTOR SPINOR FOR RIEMANNIAN FOLIATIONS
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 Title & Authors
THE PROPERTIES OF THE TRANSVERSAL KILLING SPINOR AND TRANSVERSAL TWISTOR SPINOR FOR RIEMANNIAN FOLIATIONS
Jung, Seoung-Dal; Moon, Yeong-Bong;
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 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;
 Language
English
 Cited by
1.
TRANSVERSAL KILLING AND TWISTOR SPINORS ASSOCIATED TO THE BASIC DIRAC OPERATORS, Reviews in Mathematical Physics, 2013, 25, 08, 1330011  crossref(new windwow)
 References
1.
J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194 crossref(new window)

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. F. Glazebrook and F. W. Kamber, Transversal Dirac families in Riemannian foliations, Comm. Math. Phys. 140 (1991), 217-240 crossref(new window)

7.
K. Habermann, Twistor spinors and their zeros, J. Geom. Phys. 14 (1994), 1-24 crossref(new window)

8.
J. J. Hebda, Curvature and focal points in Riemannian foliation, Indiana Univ. Math. J. 35 (1986), 321-331

9.
S. D. Jung, The first eigenvalue of the transversal Dirac operator, J. Geom. Phys. 39 (2001), 253-264 crossref(new window)

10.
S. D. Jung, Basic Dirac operator and transversal twister operator,, Proceedings of the Eighth International Workshop on Differential Geometry 8 (2004), 157-169

11.
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

12.
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 crossref(new window)

13.
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

14.
H. B. Lawson, Jr. and M. L. Michelsohn, Spin geometry, Princeton Univ. Press, Princeton, New Jersey, 1989

15.
A. Lichnerowicz, On the twistor-spinors, Lett. Math. Phys. 18 (1989), 333-345 crossref(new window)

16.
P. March, M. Min-Oo, and E. A. Ruh, Mean curvature of Riemannian foliations, Canad. Math. Bull. 39 (1996), 95-105 crossref(new window)

17.
A. Mason, An application of stochastic flows to Riemannian foliations, Houston J. Math. 26 (2000), 481-515

18.
E. Park and K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1996), 1249-1275 crossref(new window)

19.
R. Penrose and W. Rindler, Spinors and Space Time, Cambr. Mono. in Math. Physics, 2 (1986)

20.
Ph. Tondeur, Foliations on Riemannian manifolds, Springer-Verlag, New-York, 1988