Analytic formulas for complete hyperbolic affine spheres

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Date

2013

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Advisor

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Publisher

Cambridge : arXiv

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Link to publishers' Version

http://arxiv.org/abs/1305.4814

Abstract

We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of these cones. The affine spheres are represented by explicit hypersurface immersions into three-dimensional real space. The generic member of the family of immersions is given by elliptic integrals.

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Keywords

Affine differential geometry, affine spheres, analytic expressions, Monge-Amp`ere equation

Keywords GND

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Publication Type

Report

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publishedVersion

URI

https://oa.tib.eu/renate/handle/123456789/2757

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Mathematik

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