Publication details

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


SLOVÁK Jan CAP Andreas SOUČEK Vladimír

Year of publication 2000
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords invariant operators; Hermitian symmetric spaces; parabolic geometry; standard operators
Description 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. 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, these formulae are universal for all geometries in question.
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