Andreas Cap, Jan Slovak, Vladimr Soucek
Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, I. Invariant Differentiation
The paper is published:
Acta Math. Univ. Comenianae 66, 1 (1997) 33-69
- MSC:
- 53A30 Conformal differential geometry
- 53A40 Other special differential geometries
- 53B15 Other connections
- 53C10 $G$-structures
- 58A20 Jets
- 22E46 Semisimple Lie groups and their representations
- 53A20 Projective differential geometry
- 53C35 Symmetric spaces, See also {32M15, 57T15}
Abstract: 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.
Keywords: AHS structure, conformal structure, projective structure, quaternionic structure, invariant differential operator, Cartan connection
Notes: second version