Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds

Research output: Contribution to journalArticle

12 Citations (Scopus)

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
Externally publishedYes

Fingerprint

Enveloping Algebra
Algebra
Riemannian Manifold
Curvature
Gradient
Vanishing Theorems
Riemannian Metric
Differential operator
First-order

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds. / Homma, Yasushi.

In: Transactions of the American Mathematical Society, Vol. 358, No. 1, 01.2006, p. 87-114.

Research output: Contribution to journalArticle

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