Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds

Yasushi Homma

doi:10.1090/S0002-9947-05-04068-7

Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds

Yasushi Homma^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 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 language	English
Pages (from-to)	87-114
Number of pages	28
Journal	Transactions of the American Mathematical Society
Volume	358
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-05-04068-7
Publication status	Published - 2006 Jan
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-05-04068-7

Cite this

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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-Weitzenb{\"o}ck formulas for gradients. As applications, we give some vanishing theorems.",

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AB - 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.

KW - Bochner-weitzenböck formulas

KW - Casimir elements

KW - Invariant operators

KW - SO(n)-modules

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Bochner-weitzenböck formulas and curvature actions on Riemannian manifolds

Abstract

Keywords

ASJC Scopus subject areas

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