invariant operators; Cartan connection; almost hermitian symmetric structures
The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type $G/B$ which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup $B$ of the Lie group $G$. One example of an operator of this type is the Penrose's local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more details.
Baston R.: Almost hermitian symmetric manifolds I, Local twistor theory
. Duke Math. Journal 63.1 81-112 (1991). MR 1106939
| Zbl 0724.53019
Baston R.: Almost hermitian symmetric manifolds II, Differential invariants
. Duke Math. Journal 63.2 113-138 (1991). MR 1106940
| Zbl 0724.53020
Bailey T.N., Eastwood M.G.: Complex paraconformal manifolds; their differential geometry and twistor theory
. Forum Mathematicum 3 61-103 (1991). MR 1085595
| Zbl 0728.53005
Bailey T.N., Eastwood M.R., Gover A.R.: Thomas structure bundle for conformal, projective and related structures. preprint.
Čáp A., Slovák J., Souček V.: Invariant operators on manifolds with almost hermitian symmetric structures, I,II. preprints of Schrödinger Institute, Vienna, 1994.
Delanghe R., Sommen F., Souček V.: Clifford Algebra and Spinor-valued Functions
. Kluwer, 1992. MR 1169463
Ochiai T.: Geometry associated with semisimple flat homogeneous spaces
. Trans. Amer. Math. Soc. 152 159-193 (1970). MR 0284936
| Zbl 0205.26004
Kostant B.: Lie algebra cohomology and the generalized Borel-Weil theorem
. Ann. Math 74 329-387 (1961). MR 0142696
| Zbl 0134.03501