The Bochner identities for the Kählerian gradients

2002/07/03 by Yasushi Homma, Homma, Yasushi
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT) #math.DG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0207031

49 pages, LaTeX2e

arxiv created 2002/07/03 · arxiv updated 2009/11/30

Abstract

We discuss algebraic properties for the symbols of geometric first order differential operators on almost Hermitian manifolds and Kähler manifolds. Through study on the universal enveloping algebra and higher Casimir elements, we know algebraic relations for the symbols like the Clifford algebra. From the relations, we have all the Bochner identities for the operators. As applications, we have vanishing theorems, the Bochner-Weitzenböck formula, and eigenvalue estimates for the operators on Kähler manifolds.

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