The Hijazi inequality on manifolds with boundary

Simon Raulot (1)

1 IECN - Institut Élie Cartan de Nancy

In this paper, we prove the Hijazi inequality on compact Riemannian spin manifolds under two boundary conditions: the condition associated with a chirality operator and the Riemannian version of the $\MIT$ bag condition. We then show that the limiting-case is characterized as being a half-sphere for the first condition whereas the equality cannot be achieved for the second.

Mots clés: Manifolds with Boundary; Dirac Operator; Conformal Geometry; Spectrum; Yamabe Problem

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. The Hijazi inequality on manifolds with boundary. Journal of Geometry and Physics, 2006, 56, No. 11, p. 2189-2202. ⟨hal-00021460⟩