Extrinsic Bounds for Eigenvalues of the Dirac Operator
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 1998
 arXiv:
 arXiv:math/9805064
 Bibcode:
 1998math......5064B
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Spectral Theory;
 58G25;
 53C42
 EPrint:
 24 pages, LaTeX2e. to appear in Ann. Glob. Anal. Geom