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Peetre-Slovak's theorem revisited
AbstractIn 1960, J. Peetre proved the finiteness of the order of linear local operators. Lateron, J. Slov´ak vastly generalized this theorem, proving the finiteness of the order of abroad class ofExpand
Moduli spaces for finite-order jets of Riemannian metrics
Publicado en: Differential Geometry and its Applications, Volume 28, Issue 6, Dec 2010, pages 672-688 DOI: 10.1016/j.difgeo.2010.07.002
Lovelock's theorem revisited
Let (X,g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock ([4], [5], [6]) gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy theExpand
On moduli spaces for finite-order jets of linear connections
We describe the ringed-space structure of moduli spaces of jets of linear connections (at a point) as orbit spaces of certain linear representations of the general linear group. Then, we use thisExpand
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 byExpand
Uniqueness of the Gauss–Bonnet–Chern formula (after Gilkey–Park–Sekigawa)
Abstract On an oriented Riemannian manifold, the Gauss–Bonnet–Chern formula establishes that the Pfaffian of the metric represents, in de Rham cohomology, the Euler class of the tangent bundle.Expand
On second-order, divergence-free tensors
The aim of this paper is to describe the vector spaces of those second-order tensors on a pseudo-Riemannian manifold (i.e., tensors whose local expressions only involve second derivatives of theExpand
On the uniqueness of the torsion and curvature operators
We use the theory of natural operations to characterise the torsion and curvature operators as the only natural operators associated to linear connections that satisfy the Bianchi identities.
Natural operations on holomorphic forms
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 exteriorExpand
On the naturalness of Einstein’s equation
We compute all 2-covariant tensors naturally constructed from a semiriemannian metric g which are divergence-free and have weight greater than 2. As a consequence, it follows a characterization ofExpand
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