Eigenvalue estimates for the Dirac-Schrödinger operators

Abstract

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-Schrödinger operator D_f = D - f/2.

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

References in corpus (2)

• On the Spinor Representation of Surfaces in Euclidean 3-Space
• The Einstein-Dirac Equation on Riemannian Spin Manifolds

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• The energy-momentum tensor as a second fundamental form
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• Lower bounds for the eigenvalue estimates of the submanifold Dirac operator
• A spinorial approach to constant scalar curvature hypersurfaces in pseudo-hyperbolic manifolds
• A new extrinsic estimate for the spectrum of the Dirac operator
• Integrating Factors for Dirac-Schrodinger Operators: Improving Eigenvalue Estimates and Applications to Charged Positive Mass Theorems Outside Horizon(s)
• Dirac operators on lightlike hypersurfaces
• Remarks on the spectrum of the Dirac operator
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