A characterization of hyperbolic affine flat, affine minimal surfaces in \(\mathbb{A}^3\)

DOI10.1016/J.DIFGEO.2014.08.003zbMath1301.53009arXiv1308.0288OpenAlexW2963918182WikidataQ115356165 ScholiaQ115356165MaRDI QIDQ744144

Jonah M. Miller, Jeanne Nielsen Clelland

Publication date: 6 October 2014

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.0288

zbMATH Keywords

method of moving frameshyperbolic surfaceimproper affine sphereaffine flat surfaceaffine minimal surfaceequiaffine space

Mathematics Subject Classification ID

Exterior differential systems (Cartan theory) (58A15) Affine differential geometry (53A15)

Cites Work

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• Flat affine spheres in \(R^ 3\)
• Affine variation formulas and affine minimal surfaces
• An algebraic representation of the affine Bäcklund transformation
• An analogue of Bäcklund's theorem in affine geometry
• Improper affine spheres in \(\mathbb{R}^ 3\) and \(\mathbb{C}^ 3\)
• Affine minimal hypersurfaces of rotation
• Singly-periodic improper affine spheres.
• Symmetry and uniqueness of parabolic affine spheres
• The Cauchy problem for improper affine spheres and the Hessian one equation

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