2003/07/02 by Yasushi Homma, Homma, Yasushi
Mathematics · #17B35 #53B20 #58J60 #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT) #math.DG #math.RT #msc:17B35 #msc:53B20 #msc:58J60
paper · pdf · doi:10.48550/arxiv.math/0307022
This paper is a new version of math.DG/0007052, containing new results
arxiv created 2003/07/02 · arxiv updated 2009/11/30
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-Weitzenböck formulas for gradients. As applications, we give some vanishing theorems.