Extrinsic Bounds for Eigenvalues of the Dirac Operator

Details Extrinsic Bounds for Eigenvalues of the Dirac Operator Extrinsic Bounds for Eigenvalues of the Dirac Operator

1998-05-13

arxiv.org/abs/math/9805064v1

Ann. Glob. Anal. Geom. 16 , 573-596 (1998)

Mathematics

Differential Geometry

24 pages, LaTeX2e. to appear in Ann. Glob. Anal. Geom

Scientific paper

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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