### Affine spheres with constant affine sectional cuvature.

Udo Simon, An-Mi Li, Luc Vrancken (1991)

Mathematische Zeitschrift

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Udo Simon, An-Mi Li, Luc Vrancken (1991)

Mathematische Zeitschrift

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Bobenko, Alexander I., Schief, Wolfgang K. (1999)

Experimental Mathematics

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Luc Vrancken (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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R. Niebergall, P.J. Ryan (1994)

Mathematische Zeitschrift

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H. Z. Li (2005)

Banach Center Publications

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This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss variational problems in equiaffine differential geometry, centroaffine differential geometry and relative differential geometry, which have been studied by Blaschke [Bla], Chern [Ch], C. P. Wang [W], Li-Li-Simon [LLS], and Calabi [Ca-II]. We first derive the Euler-Lagrange equations in these settings; these equations are complicated, strongly nonlinear fourth order...

An-Min Li, Fang Jia (2005)

Banach Center Publications

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This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.

Wegner, Bernd (1990)

Portugaliae mathematica

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Stefan Ivanov (1997)

Monatshefte für Mathematik

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L. Ferrer, A. Martinez, F. Milán (1996)

Mathematische Annalen

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Józef Joachim Telega (1977)

Annales Polonici Mathematici

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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.

Gardner, Robert B., Wilkens, George R. (1997)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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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.

Cruceanu, Vasile (2005)

Balkan Journal of Geometry and its Applications (BJGA)

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Waldemar Cieślak, Elzbieta Szczygielska (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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A family of regular annuli is considered. Affine invariants of annuli are introduced.