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 Kähler submanifolds in Kähler manifolds carrying Kählerian Killing spinors. We then compute the spectrum of the twisted Dirac operator of the canonical embedding CPd ! CPn in order to test the sharpness
of the upper bounds.