Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14741
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Main Title: Three dimensional affine hyperspheres generated by 2-dimensional partial differential equations
Author(s): Vrancken, Luc
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15968
http://dx.doi.org/10.14279/depositonce-14741
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: It is well known that locally strongly convex affine hyperspheres can be determined as solutions of differential euqations of Monge-Ampere type. In this paper we study in partivular the 3-dimensional case and we assume that the hypersphere admits a Killing vector field (with respect to the affine metric) whose integral curves are geodesics with respect to both the induced affine connection and the Levi Civita connection of the affine metric. We show that besides the already known examples, such hyperspheres can be constructed starting from the 2-dimensional Laplace equation, the 2-dimensional sine-Gordon equation or the 2-dimensional cosh-Gordon equation.
Subject(s): affine differential geometry
Issue Date: 1-Feb-2000
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 53A15 Affine differential geometry
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2000, 662
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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