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ISSN 1088-6850(e) ISSN 0002-9947(p)

Bochner-Weitzenböck formulas and curvature actions on Riemannian manifolds

Author: Yasushi Homma
Journal: Trans. Amer. Math. Soc. 358 (2006), 87-114
MSC (2000): Primary 53B20, 58J60, 17B35
Posted: August 25, 2005
MathSciNet review: 2171224
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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.

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