Dual Connections and Affine Geometry.
Takashi Kurose (1990)
Mathematische Zeitschrift
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Takashi Kurose (1990)
Mathematische Zeitschrift
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Miloš Božek (1982)
Colloquium Mathematicae
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John Smillie (1981)
Inventiones mathematicae
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R. S. Mishra (1972)
Colloquium Mathematicae
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Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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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.
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.
Varga, Adrienn (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Ivan Kolář, Marco Modugno (1990)
Czechoslovak Mathematical Journal
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Karáné, G.S. (1994)
Beiträge zur Algebra und Geometrie
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Manindra Chandra Chaki (1956)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.