A complete minimal Klein bottle in \(\mathbb{R}^ 3\)
type: Item
instance of: scholarly article
title: A complete minimal Klein bottle in \(\mathbb{R}^ 3\)
zbMATH Open document ID: 0796.53006
DOI: 10.1215/S0012-7094-93-07102-5
author: Francisco J. López
published in: Duke Mathematical Journal
publication date: 1994-09-26T00:00:00Z
review text: The author studies complete nonorientable minimal surfaces in \(\mathbb{R}^ 3\) with finite total curvature. For a long time, the only known nonorientable minimal surface was Henneberg's surface, which is not regular. Later, Meeks exhibited a minimal Möbius strip with total curvature \(C= -6\pi\). In this paper, a new important example is constructed, a minimal Klein bottle with \(C= -8\pi\). Geometrically, this surface is obtained by attaching a Klein bottle to the Enneper surface. In a forthcoming paper, the author will publish a uniqueness theorem and a classification of all complete minimal surfaces with \(C> -10\pi\).
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 495435
zbMATH Keywords: nonorientable minimal surfaces
zbMATH Keywords: finite total curvature
zbMATH Keywords: minimal Klein bottle
zbMATH Keywords: Enneper surface
reviewed by: Fritz Gackstatter
MaRDI profile type: Publication
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full work available at URL: s0012-7094-93-07102-5
OpenAlex ID: W1544766413
description: scientific article; zbMATH DE number 495435