Advanced SearchSearch Tips
Eigenvalues of Type r of the Basic Dirac Operator on Kähler Foliations
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 3,  2013, pp.333-340
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.3.333
 Title & Authors
Eigenvalues of Type r of the Basic Dirac Operator on Kähler Foliations
Jung, Seoung Dal;
  PDF(new window)
In this paper, we prove that on a Khler spin foliatoin of codimension $q
Transversal(basic) Dirac operator;Khler spin foliation;
 Cited by
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)

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, October 1988.

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

G. Habib, Eigenvalues of the transversal Dirac operator on Kahler foliations, J. Geom. Phys., 56(2006), 260-270. crossref(new window)

G. Habib and K. Richardson, A brief note on the spectrum of the basic Dirac operator, Bull. London Mah. Soc., 41(2009), 683-690. crossref(new window)

S. D. Jung, Eigenvalue estimate of the basic Dirac operator on a Kahler foliation, Diff. Geom. Appl., 24(2006), 130-141. crossref(new window)

S. D. Jung and T. H. Kang, Lower bounds for the eigenvalue of the transversal Dirac operator on a Kahler foliation, J. Geom. Phy., 45(2003), 75-90. crossref(new window)

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.

K. D. Kirchberg, An estimation for the first eigenvalue of the Dirac operator on closed Kahler manifolds of positive scalar curvature, Ann. Glob. Anal. Geom., 4(1986), 291-325. crossref(new window)

K. D. Kirchberg, The first eigenvalue of the Dirac operator on Kahler manifolds, J. Goem. Phys., 7(1990), 449-468. crossref(new window)

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

S. Nishikawa, Ph. Tondeur, Transversal infinitesimal automorphisms for harmonic Kahler foliations, Tohoku Math. J., 40(1988), 599-611. crossref(new window)

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

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