On the affine rectification of convex curves.

Leichtweiss, Kurt

Displaying similar documents to “On the affine rectification of convex curves.”

Bifurcations of affine invariants for one-parameter family of generic convex plane curves

Takashi Sano (1999)

Banach Center Publications

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We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.

Remark on the equisingularity of families of affine plane curves

Hà Huy Vui, Phạkm Tien Son (1998)

Annales Polonici Mathematici

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We give some criteria for the equisingularity of families of affine plane curves.

Affine Curves in Characteristic p.

Werner Lütkebohmert (1980)

Mathematische Zeitschrift

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Affine differential invariants for planar curves.

Nadjafikhah, Mehdi (2002)

Balkan Journal of Geometry and its Applications (BJGA)

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On affine geometric product objects

Józef Joachim Telega (1977)

Annales Polonici Mathematici

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Curvature functionals for curves in the equi-affine plane

Steven Verpoort (2011)

Czechoslovak Mathematical Journal

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After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.

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.

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.

Research works of Romanian mathematicians on centro-affine geometry.

Cruceanu, Vasile (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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On a functional equation containing four weighted arithmetic means.

Varga, Adrienn (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Affine Curves in Characteristic p are Set Theoretic Complete Intersections.

R.C. Cowsik, M.V. Nori (1978)

Inventiones mathematicae

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General-affine invariants of plane curves and space curves

Shimpei Kobayashi, Takeshi Sasaki (2020)

Czechoslovak Mathematical Journal

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We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups $GA (2) = GL (2, ℝ) ⋉ ℝ^{2}$ and $GA (3) = GL (3, ℝ) ⋉ ℝ^{3}$ , respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and...