Geodesic
INVARIANT OPERATORS ON MANIFOLDS WITH ALMOST HERMITIAN SYMMETRIC STRUCTURES, I. INVARIANT DIFFERENTIATION
Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1 
A. Cap; J. Slovak; V. Soucek. INVARIANT OPERATORS ON MANIFOLDS WITH ALMOST HERMITIAN SYMMETRIC STRUCTURES, I. INVARIANT DIFFERENTIATION. Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a2/
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     title = {INVARIANT {OPERATORS} {ON} {MANIFOLDS} {WITH} {ALMOST} {HERMITIAN} {SYMMETRIC} {STRUCTURES,} {I.} {INVARIANT} {DIFFERENTIATION}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1997},
     volume = {66},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a2/}
}
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This is the first part of a series of three papers. The whole series aims to develop the tools for the study of all almost Hermitian symmetric structures in a unified way. In particular, methods for the construction of invariant operators, their classification and the study of their properties will be worked out. In this paper we present the invariant differentiation with respect to a Cartan connection and we expand the differentials in the terms of the underlying linear connections belonging to the structures in question. Then we discuss the holonomic and non-holonomic jet extensions and we suggest methods for the construction of invariant operators.