The twisted Spin${}^c$ Dirac operator on K\"ahler submanifolds of the complex projective space

In this paper, we estimate the eigenvalues of the twisted Dirac operator on K"ahler submanifolds of the complex projective space $C{P}^m$ and we discuss the sharpness of this estimate for the embedding $C{P}^d\hookrightarrow C{P}^m$.