Affine isoperimetric problems and surfaces with constant affine mean curvature.
F. Milán, A. Martínez (1992)
Manuscripta mathematica
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F. Milán, A. Martínez (1992)
Manuscripta mathematica
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M. Magid, C. Scharlach, L. Vrancken (1995)
Manuscripta mathematica
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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.
F. Milán, A. Martínez (1991)
Mathematische Zeitschrift
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Katsumi Nomizu, Takeshi Sasaki (1990)
Manuscripta mathematica
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Cruceanu, Vasile (2005)
Balkan Journal of Geometry and its Applications (BJGA)
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Mikio Furushima (1989)
Mathematische Annalen
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Józef Joachim Telega (1977)
Annales Polonici Mathematici
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Takashi Kurose (1990)
Mathematische Zeitschrift
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Luc Vrancken (1996)
Monatshefte für Mathematik
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R.V. Gurjar, A.R. Shastri (1984)
Commentarii mathematici Helvetici
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Michał Sadowski (1990)
Colloquium Mathematicae
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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.
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.