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Lower Bounds for the Eigenvalues of the Dirac Operator on Spin\({}^c\) Manifolds

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Abstract

In this paper, we generalize lower bound estimates for the eigenvalue of the Dirac operator defined on compact Riemannian Spin\({}^c\)-manifold proved by R. Nakad 2010. Then, we improve our estimates in terms of the first eigenvalue of the Yamabe number and energy–momentum tensor.

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Correspondence to Serhan Eker.

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Eker, S. Lower Bounds for the Eigenvalues of the Dirac Operator on Spin\({}^c\) Manifolds. Iran J Sci Technol Trans Sci 44, 251–257 (2020). https://doi.org/10.1007/s40995-020-00823-5

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Keywords

  • Spin and Spin\({}^c\) geometry
  • Dirac operator
  • Estimation of eigenvalues

Mathematics Subject Classification

  • 53C27
  • 34L40
  • 35P15