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

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Using Weitzenböck 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.
Latex2.09, 14 pages

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Differential Geometry, 53C27, 53C25

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http://salesiana.dossiersoluciones.com/handle/123456789/63225

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201279
 http://arxiv.org/abs/math/0201279

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arXiv