On totally real embeddings into \({\mathbb{C}}^ n\)
type: Item
instance of: scholarly article
title: On totally real embeddings into \({\mathbb{C}}^ n\)
zbMATH Open document ID: 0597.57018
author: Franc Forstnerič
published in: Expositiones Mathematicae
publication date: 1986-01-01T00:00:00Z
review text: An immersion \(f: M^ m\to {\mathbb{C}}^ n\) is totally real if for each \(p\in M\) the tangent space to f(M) at f(p) contains no nontrivial complex linear subspace (so \(m\geq n)\). The main result of this paper states that when \(m=n\geq 3\), any totally real immersion which is regularly homotopic to an embedding is regularly homotopic through a family of totally real immersions to a totally real embedding. Some applications are given, for example it is shown that every compact orientable 3-manifold admits a totally real embedding in \({\mathbb{C}}^ 3\).
Mathematics Subject Classification ID: 57R40
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 32K15
zbMATH DE Number: 3962778
zbMATH Keywords: embedding manifolds in complex n-space
zbMATH Keywords: totally real immersion
zbMATH Keywords: regularly homotopic to an embedding
zbMATH Keywords: totally real embedding
zbMATH Keywords: compact orientable 3- manifold
reviewed by: David B. Gauld
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3962778