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 A note on generalized Dirac eigenvalues for split holonomy and torsion Bull. Korean Math. Soc. 2014 Vol. 51, No. 6, 1579-1589 https://doi.org/10.4134/BKMS.2014.51.6.1579Published online November 30, 2014 Ilka Agricola and Hwajeong Kim Hans-Meerwein-Strasse, Hannam University 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 MSC numbers : 53C25, 53C26, 53C27, 53C28, 53C29, 58J50, 58J60 Downloads: Full-text PDF