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Displaying similar documents to “∇-flat functions on manifolds”

Affinely equivalent complete flat manifolds

Michal Sadowski (2004)

Open Mathematics

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Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).

A remark on semi-∇-flat functions

Wojciech Kozłowski (2006)

Annales Polonici Mathematici

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We give a pointwise characterization of semi-∇-flat functions on an affine manifold (M,∇).

On Metrizable Locally Homogeneous Connections in Dimension

Alena Vanžurová (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We discuss metrizability of locally homogeneous affine connections on affine 2-manifolds and give some partial answers, using the results from [Arias-Marco, T., Kowalski, O.: Classification of locally homogeneous affine connections with arbitrary torsion on 2-dimensional manifolds. Monatsh. Math. 153 (2008), 1–18.], [Kowalski, O., Opozda, B., Vlášek, Z.: A classification of locally homogeneous connections on 2-dimensional manifolds vis group-theoretical approach. CEJM 2, 1 (2004), 87–102.],...

Some results on projectively flat affine surfaces

Antonio Martínez, Francisco Milán (2005)

Banach Center Publications

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We focus our attention on projectively flat affine surfaces. First, we classify the affine surfaces with projectively flat induced connection and constant Pick invariant. We also investigate the compact case and study how the geometry at the boundary determines the geometry of the surface.