The Hijazi inequalities on complete Riemannian $Spin^c$ 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 complete Riemannian Spin^c manifolds of finite volume and without boundary. Under some additional assumptions and using the refined Kato inequality, we prove the Hijazi inequality for elements of the essential spectrum. The limiting cases are also studied.

Mots clés: Eigenvalues; Dirac operator; Spin^c structures; Conformal geometry; Perturbed Yamabe operator; Energy-Momentum tensor; Refined Kato inequality; Refined Kato inequality.

Domaines: Géométrie différentielle [math.DG]

Roger Nakad. The Hijazi inequalities on complete Riemannian $Spin^c$ manifolds. Advances in Mathematical Physics, 2011, 2011, pp.471810. ⟨10.1155/2011/471810⟩. ⟨hal-00493061v2⟩