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A NOTE ON GENERALIZED DIRAC EIGENVALUES FOR SPLIT HOLONOMY AND TORSION

  • Agricola, Ilka (Fachbereich Mathematik und Informatik Philipps-Universitat Marburg) ;
  • Kim, Hwajeong (Department of Mathematics Hannam University)
  • Received : 2013.05.22
  • Published : 2014.11.30

Abstract

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

Acknowledgement

Supported by : NRF(National Research Foundation of Korea)

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