Geometry of isotypic Kronecker webs

Wojciech Kryński

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Grassmannian structures on manifolds.

Dhooghe, P.F. (1994)

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Connection theory on differentiable fibre bundles: A concise introduction.

Iliev, Bozhidar Z. (2006)

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Natural operators in the view of Cartan geometries

Martin Panák (2003)

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We prove, that $r$ -th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1, 0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r - 1$ . On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem...

G-connections as twisted formal solutions of systems of PDE's related to geometric structures

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Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr

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Given a fibered manifold $Y \to X$ , a 2-connection on $Y$ means a section $J^{1} Y \to J^{2} Y$ . The authors determine all first order natural operators transforming a 2-connection on $Y$ and a classical linear connection on $X$ into a connection on $J^{1} Y \to Y$ . (The proof implies that there is no first order natural operator transforming 2-connections on $Y$ into connections on $J^{1} Y \to Y$ .) Using this result, the authors deduce several properties of characterizable connections on $J^{1} Y \to X$ .