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Extrinsic eigenvalue estimates of the Dirac operator

Daguang Chen
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Abstract

For a compact spin manifold $M$ isometrically embedded into Euclidean space, we derive the extrinsic estimates from above and below for eigenvalues of the Dirac operators, which depend on the second fundamental form of the embedding. We also show the bounds of the ratio of the eigenvalues.

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Daguang Chen. 2007-01-29. Extrinsic eigenvalue estimates of the Dirac operator. https://arxiv.org/abs/math/0701847

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