The Hijazi inequalities on complete Riemannian \(\mathrm{Spin}^c\) manifolds (Q541164)

Summary: We extend the Hijazi type inequality, involving the energy-momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian \(\text{Spin}^c\) manifolds without boundary and of finite volume. Under some additional assumptions, using the refined Kato inequality, we prove the Hijazi-type inequality for elements of the essential spectrum. The limiting cases are also studied.