Examples of minimal unit vector fields
type: Item
instance of: scholarly article
title: Examples of minimal unit vector fields
zbMATH Open document ID: 1005.53026
DOI: 10.1023/A:1006788819180
published in: Annals of Global Analysis and Geometry
publication date: 2003-02-17T00:00:00Z
review text: The main purpose of the paper under review is to present a series of examples of Riemannian manifolds equipped with a minimal unit vector field. These examples belong to the following classes of Riemannian manifolds: \(2\)-dimensional manifolds; \(3\)-dimensional manifolds; semi-direct products \(\mathbb{R} \times _{\alpha} \mathbb{R}\), where \(\alpha : \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}\) is a linear map; warped products \(\mathbb{R} \times _{f} M\) of the one-dimensional Euclidean space \(\mathbb{R}\) and the \(n\)-dimensional Riemannian manifold; doubly warped products \(\mathbb{R} \times _{f} M_{1} \times _{g} M_{2}\), K-contact manifolds; contact metric \((k,\mu)\)-spaces; Kenmotsu manifolds; the generalized Heisenberg groups \(H(1,r)\) (introduced by Y. Haraguchi); generalized Heisenberg groups (introduced by A. Kaplan) and the Damek-Ricci spaces. Let us mention that the Damek-Ricci spaces provided the first class of examples of harmonic spaces which are not locally symmetric.
reviewed by: Ryszard Deszcz
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1530059
zbMATH Keywords: geodesic
zbMATH Keywords: normal
zbMATH Keywords: strongly normal and minimal vector fields
author: J. C. González-Dávila
author: Lieven Vanhecke
MaRDI profile type: Publication
full work available at URL: a:1006788819180
OpenAlex ID: W1607423200
description: scientific article; zbMATH DE number 1530059