A relation between the Ricci tensor and the spectrum of the Dirac operator

Details A relation between the Ricci tensor and the spectrum of the Dirac operator A relation between the Ricci tensor and the spectrum of the Dirac operator

2002-01-29

arxiv.org/abs/math/0201279v1

Mathematics

Differential Geometry

Latex2.09, 14 pages

Scientific paper

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive a general inequality depending on a real parameter and joining the spectrum of the Dirac operator with terms depending on the Ricci tensor and its first covariant derivatives. The discussion of this inequality yields vanishing theorems for the kernel of the Dirac operator $D$ and new lower bounds for the spectrum of $D^2$ if the Ricci tensor satisfies certain conditions.

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