The Hijazi inequality on manifolds with boundary
arXiv:math/0603510 · doi:10.1016/j.geomphys.2005.11.013
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.
14 pages