Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds

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Abstract

Gradients are natural first order differential operators depending on Riemannian metrics. The principal symbols of them are related to the enveloping algebra and higher Casimir elements. We give formulas in the enveloping algebra that induce not only identities for higher Casimir elements but also all Bochner-Weitzenböck formulas for gradients. As applications, we give some vanishing theorems.

Original languageEnglish
Pages (from-to)87-114
Number of pages28
JournalTransactions of the American Mathematical Society
Volume358
Issue number1
DOIs
Publication statusPublished - 2006 Jan 1

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Keywords

  • Bochner-weitzenböck formulas
  • Casimir elements
  • Invariant operators
  • SO(n)-modules

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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