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 $\nabla$ with skew torsion $T\in\Lambda^3M$ 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 Killing equation with torsion and use it to discuss the case in which the minimum is attained in the bound. 
Ilka Agricola, Julia Becker-Bender, Hwajeong Kim
math.DG hep-th math-ph math.MP