Advances in Mathematical Physics
Volume 2011 (2011), Article ID 471810, 14 pages
doi:10.1155/2011/471810
Research Article

The Hijazi Inequalities on Complete Riemannian S p i n c Manifolds

Institut Élie Cartan, Université Henri Poincaré, Nancy I, B.P 239, 54506 Vandœuvre-Lès-Nancy Cedex, France

Received 20 December 2010; Accepted 21 January 2011

Academic Editor: Andrei Moroianu

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.

Abstract

We extend the Hijazi type inequality, involving the energy-momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spi n 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.