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Eigenvalues of Type r of the Basic Dirac Operator on Kähler Foliations

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경북대학교 자연과학대학 수학과|2013.09|Kyungpook Mathematical Journal|제53권 제3호|pp. 333-340

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참고문헌

키워드

Transversal(basic) Dirac operatorKahler spin foliation
주제분류수학

초록

In this paper, we prove that on a K¨ahler spin foliatoin of codimension q = 2n,any eigenvalue λ of type r (r ∈ {1, · · · , [ n+1/2 ]}) of the basic Dirac operator Db satisfies theinequality λ2 ≥ r/4r−2 infM σ∇, where σ∇ is the transversal scalar curvature of F.

Abstract

In this paper, we prove that on a K¨ahler spin foliatoin of codimension q = 2n,any eigenvalue λ of type r (r ∈ {1, · · · , [ n+1/2 ]}) of the basic Dirac operator Db satisfies theinequality λ2 ≥ r/4r−2 infM σ∇, where σ∇ is the transversal scalar curvature of F.

참고문헌 (14)

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  9. K. D. Kirchberg, "An estimation for the first eigenvalue of the Dirac operator on closed K¨ahler manifolds of positive scalar curvature", Ann. Glob. Anal. Geom., 4, pp.291~325 (1986)
  10. K. D. Kirchberg, "The first eigenvalue of the Dirac operator on K¨ahler manifolds", J. Goem. Phys, 7, pp.449~468 (1990)
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  12. S. Nishikawa, "Transversal infinitesimal automorphisms for harmonic K¨ahler foliations", Tohoku Math. J., 40, pp.599~611 (1988)
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  14. Ph. Tondeur, "Foliations on Riemannian manifolds" (1988), Springer-Verlag

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