Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P 239,
54506 Vandœuvre-Lès-Nancy Cedex, France
Copyright © 2011 Roger Nakad. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We extend the Hijazi type inequality, involving the energy-momentum
tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spi 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.