# The Hijazi inequality on manifolds with boundary

Research paper by Simon Raulot

Indexed on: 21 Mar '06Published on: 21 Mar '06Published in: Mathematics - Differential Geometry

#### Abstract

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.