A note on generalized Dirac eigenvalues for split holonomy and torsion

Abstract

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\in {\Lambda }^{3}M$ 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.

to appear in Bulletin of the Korean Mathematical Society

References in corpus (3)

• The Srni lectures on non-integrable geometries with torsion
• On types of non-integrable geometries
• Almost Hermitian Structures with Parallel Torsion