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Main Title: Affine surfaces in 4-dimensional affine space with planar geodesics
Author(s): Vrancken, Luc
Type: Research Paper
Abstract: In this paper we study nondegenerate affine immersions, as introduced by Nomizu and Pinkall, of an affine surface $(M,\nabla)$ in the 4-dimensional affine space $(\mathbb{R}^4,D)$. Using an existence and uniqueness theorem, we classify all such immersions $\phi$ which map the $\nabla$-geodesics of $M$ into planar curves in $\mathbb{R}^4$. These theorems generalize results previously obtained in the Riemannian, the equiaffine and the centroaffine case.
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, 663
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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