A short proof of eigenvalue estimates for the Dirac operator on Riemannian and K\"ahler manifolds

Uwe Semmelmann

E-mail: semmelma@rz.mathematik.uni-muenchen.de

Abstract. Aim of this note is to present short and natural proofs for the lower bounds of the spectrum of the Dirac operator on compact Riemannian and K\"ahler manifolds with positive scalar curvature.

AMSclassification. Primary 53A50; Secondary 58G25, 58G30

Keywords. Dirac operators, eigenvalue, lower bound