Eigenvalue estimates for the Dirac-Schrodinger operators

We give new estimates for the eigenvalues of the hypersurface Dirac operato r in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the l imiting cases of the estimates obtained by Zhang and Hijazi [Math. Res. Let t. 5 (1998) 199; 6 (1999) 465; Ann. Glob. Anal. Geom., in press]. We compar e these limiting cases with those corresponding to the Friedrich and Hijazi inequalities. We conclude by comparing these results to intrinsic estimate s for the Dirac-Schrodinger operator D-f = D - 1/2f. (C) 2001 Elsevier Scie nce B.V. All rights reserved.