Displaying similar documents to “A remark on semi-∇-flat functions”

∇-flat functions on manifolds

Wojciech Kozłowski (2004)

Annales Polonici Mathematici

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We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.

Affine bijections of C(X,I)

Janko Marovt (2006)

Studia Mathematica

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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.

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.

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).

An affine framework for analytical mechanics

Paweł Urbański (2003)

Banach Center Publications

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An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.

Self-affine fractals of finite type

Christoph Bandt, Mathias Mesing (2009)

Banach Center Publications

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In the class of self-affine sets on ℝⁿ we study a subclass for which the geometry is rather tractable. A type is a standardized position of two intersecting pieces. For a self-affine tiling, this can be identified with an edge or vertex type. We assume that the number of types is finite. We study the topology of such fractals and their boundary sets, and we show how new finite type fractals can be constructed. For finite type self-affine tiles in the plane we give an algorithm which...

Hypersurfaces with almost complex structures in the real affine space

Mayuko Kon (2007)

Colloquium Mathematicae

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We study affine hypersurface immersions f : M → ℝ 2 n + 1 , where M is an almost complex n-dimensional manifold. The main purpose is to give a condition for (M,J) to be a special Kähler manifold with respect to the Levi-Civita connection of an affine fundamental form.