Lower bounds for the eigenvalues of the Dirac operator on $Spin^C$ manifolds

Roger Nakad (1)

1 IECN - Institut Élie Cartan de Nancy

In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on Spinc manifolds without boundary. The limiting case is then studied and examples are given.

Mots clés: $Spin^C$ structures; Dirac operator; Eigenvalues; Energy-Momentum tensor; Perturbed Yamabe operator; Conformal geometry.; Conformal geometry

Domaines: Géométrie différentielle [math.DG]

Roger Nakad. Lower bounds for the eigenvalues of the Dirac operator on $Spin^C$ manifolds. 2010. ⟨hal-00466918v2⟩