Twistorial eigenvalue estimates for generalized Dirac operators with torsion

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ∇ with skew torsion T∈Λ3M by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac operator with torsion is found that generalizes Friedrich's classical Riemannian estimate. We also determine a novel twistor and the Killing equation with torsion and use it to discuss the case in which the minimum is attained in the bound.