Bochner-Weitzenb\"ock formulas and curvature actions on Riemannian manifolds
Differential Geometry
2007-05-23 v1 Representation Theory
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 certain relations in the enveloping algebra, which induce not only identities for higher Casimir elements but also all Bochner-Weitzenb\"ock formulas for gradients. As applications, we give some vanishing theorems.
Keywords
Cite
@article{arxiv.math/0307022,
title = {Bochner-Weitzenb\"ock formulas and curvature actions on Riemannian manifolds},
author = {Yasushi Homma},
journal= {arXiv preprint arXiv:math/0307022},
year = {2007}
}
Comments
This paper is a new version of math.DG/0007052, containing new results