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 $CP^m$ and we discuss the sharpness of this estimate for the embedding $CP^d \hookrightarrow CP^m$. 
Georges Habib and Roger Nakad
math.DG math.SP