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

Jung, Seoung Dal

  • Received : 2011.08.15
  • Accepted : 2012.09.17
  • Published : 2013.09.23

Abstract

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

Keywords

Transversal(basic) Dirac operator;K$\ddot{a}$hler spin foliation

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)