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Curvature dependent lower bounds for the first eigenvalue of the Dirac operator

K. -D. Kirchberg
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Abstract

Using Weitzenböck techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields vanishing theorems for the kernel of the Dirac operator $D$ and lower bounds for the spectrum of $D^2$ if the curvature satisfies certain conditions.

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K. -D. Kirchberg. 2003-10-21. Curvature dependent lower bounds for the first eigenvalue of the Dirac operator. https://doi.org/10.1016/j.geomphys.2003.11.002

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