Eigenvalue estimates for the Dirac-Schrödinger operators

Details Eigenvalue estimates for the Dirac-Schrödinger operators Eigenvalue estimates for the Dirac-Schrödinger operators

2001-01-12

arxiv.org/abs/math/0101111v1

Journal of Geometry and Physics, 38 (2001) 57-74

Mathematics

Differential Geometry

22 pages, LaTeX, to appear in Journal of Geometry and Physics

Scientific paper

We give new estimates for the eigenvalues of the hypersurface Dirac operator 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 limiting cases of the estimates obtained by X. Zhang and O. Hijazi in [13] and [10]. We compare these limiting cases with those corresponding to the Friedrich and Hijazi inequalities. We conclude by comparing these results to intrinsic estimates for the Dirac-Schr\"odinger operator D_f = D - f/2.

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