Displaying similar documents to “Variational problems and PDEs in affine differential geometry”

Affine maximal hypersurfaces

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.

Invariance groups of relative normals

Thomas Binder, Martin Wiehe (2005)

Banach Center Publications

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We investigate a two-parameter family of relative normals that contains Manhart's one-parameter family and the centroaffine normal. The invariance group of each of these normals is classified, and variational problems are studied. The results are Euler-Lagrange equations for the hypersurfaces that are critical with respect to the area functionals of the induced and semi-Riemannian volume forms and a classification of the critical hyperovaloids in the two-parameter family.

Improper affine spheres and δ-invariants

Franki Dillen, Luc Vrancken (2005)

Banach Center Publications

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We introduce an inequality for graph hypersurfaces and prove a decomposition theorem in case equality holds.

Real hypersurfaces with a special transversal vector field

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space n + 1 are studied. Some properties of the structure determined by a J-tangent transversal vector field are proved. Moreover, some generalizations of the results obtained by V. Cruceanu are given.

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.

Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space n + 1 with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of hypersurfaces with φ or η parallel relative to an induced connection are proved. Also a local characterization of these hypersurfaces is given.