Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operators

1998/12/03 by Andreas Cap, Jan Slovak, Vladimir Soucek
Mathematics · #math.DG #msc:53A20 #msc:53A30 #msc:52A40 #msc:53A55 #msc:53B15 #msc:53C15 #msc:17B10

paper · pdf

published as Diff. Geom. Appl. 12 No. 1 (2000) 51-84 · AMS-TeX, 33 pages

arxiv created 1998/12/03 · arxiv updated 2009/11/30

Abstract

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost quaternionic geometries. Exploiting some finite dimensional representation theory of simple Lie algebras, we give explicit formulae for distinguished invariant curved analogues of the standard operators in terms of the linear connections belonging to the structures in question, so in particular we prove their existence. Moreover, we prove that these formulae for k-th order standard operators, k=1,2,..., are universal for all geometries in question.

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