Complete minimal Kähler surfaces in \(\mathbb{R}^6\)
type: Item
instance of: scholarly article
title: Complete minimal Kähler surfaces in \(\mathbb{R}^6\)
zbMATH Open document ID: 0894.53049
DOI: 10.1023/A:1006591619249
author: Marcos Dajczer
author: Detlef Gromoll
published in: Annals of Global Analysis and Geometry
publication date: 1998-08-30T00:00:00Z
review text: Let \(M^n\) be a complete Kähler manifold of complex dimension \(n\geq 2\) and \(f:M^n\longrightarrow {\mathbb R}^{2n+2}\) a minimal isometric immersion of \(M^n\) in flat Euclidean space with real codimension 2. It is known that if we assume \(f\) is not holomorphic in \({\mathbb R}^{2n+2}\equiv {\mathbb C}^{n+1}\), then \(f\) must be globally complex ruled for \(n\geq 3\). The main purpose of this paper is to consider some immersions for \(n=2\). The authors construct examples to show that there exists a class of complete minimal real Kähler surfaces \(M^2\) in \({\mathbb R}^6\) which are irreducible and neither holomorphic nor complex ruled.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1136501
zbMATH Keywords: complete minimal immersion
zbMATH Keywords: real Kähler submanifold
reviewed by: Neda Bokan
MaRDI profile type: Publication
full work available at URL: a:1006591619249
OpenAlex ID: W2913158207
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description: scientific article; zbMATH DE number 1136501