Inequalities of eigenvalues for the Dirac operator on compact complex spin submanifolds in complex projective spaces

Abstract

For a compact complex spin manifold M with a holomorphic isometric embedding into the complex projective space, the authors obtain the extrinsic estimates from above and below for eigenvalues of the Dirac operator, which depend on the data of an isometric embedding of M. Further, from the inequalities of eigenvalues, the gaps of the eigenvalues and the ratio of the eigenvalues are obtained.

Keywords

Eigenvalue / Dirac operator / Yang-type inequality / Test spinor

References

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