Abstract
We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the Willmore inequality are briefly discussed. In higher codimension we obtain bounds on the eigenvalues of the Dirac operator of the submanifold twisted with the spinor bundle of the normal bundle.
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Bär, C. Extrinsic Bounds for Eigenvalues of the Dirac Operator. Annals of Global Analysis and Geometry 16, 573–596 (1998). https://doi.org/10.1023/A:1006550532236
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DOI: https://doi.org/10.1023/A:1006550532236