Natural operations on holomorphic forms

@article{Navarro2016NaturalOO,
  title={Natural operations on holomorphic forms},
  author={Alberto Navarro and Jos'e Navarro and Carlos Prieto},
  journal={arXiv: Complex Variables},
  year={2016},
  pages={239-254}
}
We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence {\it a la Galois}. 
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References

SHOWING 1-10 OF 17 REFERENCES
Natural operations on differential forms
We prove that the only natural operations between differential forms are those obtained using linear combinations, the exterior product and the exterior differential. Our result generalises work by
Natural operations on differential forms on contact manifolds
We characterize all natural linear operations between spaces of differential forms on contact manifolds. Our main theorem says roughly that such operations are built from some algebraic operators
Chern-Weil forms and abstract homotopy theory
We prove that Chern-Weil forms are the only natural differential forms associated to a connection on a principal G-bundle. We use the homotopy theory of simplicial sheaves on smooth manifolds to
Natural operations in differential geometry
I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.
On Differential Characteristic Classes of Metrics and Connections
A differential characteristic class of a geometric quantity (e.g., Riemannian or Kähler metric, connection, etc.) on a smooth manifold is a closed differential form whose components are expressed in
Complex analytic connections in fibre bundles
Introduction. In the theory of differentiable fibre bundles, with a Lie group as structure group, the notion of a connection plays an important role. In this paper we shall consider complex analytic
Representations and Invariants of the Classical Groups
1. Classical groups as linear algebraic groups 2. Basic structure of classical groups 3. Algebras and representations 4. Polynomials and tensor invariants 5. Highest weight theory 6. Spinors 7.
On the heat equation and the index theorem
A horizontal deflection winding forms a resonant retrace circuit with two series coupled retrace capacitors during a retrace interval. A controllable circuit in shunt with the second capacitor
Transformation Groups and Natural Bundles
...
1
2
...