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http://dx.doi.org/10.4134/BKMS.2014.51.6.1579

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.6, 2014 , pp. 1579-1589 More about this Journal
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.
Keywords
Dirac operator; eigenvalue estimate; metric connection with torsion;
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