The spectrum of the twisted Dirac operator on Kähler submanifolds of the complex projective space

Abstract

We establish an upper estimate for the small eigenvalues of the twisted Dirac operator on Kahler submanifolds in Kahler manifolds carrying Kahlerian Killing spinors. We then compute the spectrum of the twisted Dirac operator of the canonical embedding CP(d) -> CP(n) in order to test the sharpness of the upper bounds.