Bulletin of the
Korean Mathematical Society BKMS

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