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Extrinsic bounds for eigenvalues of the Dirac operator. (English) Zbl 0921.58065

The author derives upper eigenvalue estimates for the Dirac operator of a closed hypersurface of Euclidean space resp. a space carrying Killing spinors. In the estimates the integral over the squared mean curvature occurs and the relation with the Willmore inequality is discussed.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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