Twistorial eigenvalue estimates for generalized Dirac operators with torsion

摘要

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ?; with skew torsion T∈Λ~3M 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.