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.2014.51.6.1579
Published 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
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