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DIRAC EIGENVALUES ESTIMATES IN TERMS OF DIVERGENCEFREE SYMMETRIC TENSORS

  • Published : 2009.09.30

Abstract

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

Keywords

Dirac operator;eigenvalues;divergencefree symmetric tensors

References

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Cited by

  1. THE FIRST POSITIVE EIGENVALUE OF THE DIRAC OPERATOR ON 3-DIMENSIONAL SASAKIAN MANIFOLDS vol.50, pp.2, 2013, https://doi.org/10.4134/BKMS.2013.50.2.431
  2. Estimates of small Dirac eigenvalues on 3-dimensional Sasakian manifolds vol.28, pp.6, 2010, https://doi.org/10.1016/j.difgeo.2010.07.001
  3. Eigenvalue estimates for generalized Dirac operators on Sasakian manifolds vol.45, pp.1, 2014, https://doi.org/10.1007/s10455-013-9388-7