New examples of Riemannian manifolds with structure group \(G_ 2\)
type: Item
instance of: scholarly article
title: New examples of Riemannian manifolds with structure group \(G_ 2\)
zbMATH Open document ID: 0617.53050
DOI: 10.1007/BF02844737
author: Teresa Iglesias
author: Marisa Fernández
publication date: 1986-01-01T00:00:00Z
review text: Let W be the class of 7-dimensional manifolds having a 2-fold vector cross product [the first author and \textit{A. Gray}, Ann. Mat. Pura Appl., IV. Ser. 132, 19-45 (1982; Zbl 0524.53023)]. Let W be the space of tensors having the same symmetries as the covariant derivative \(\nabla \phi\) of the fundamental form \(\phi\) of a manifold \(M\in W\). The authors study the represention of \(G_ 2\) on W by using the theory of root systems of semisimple Lie algebras. Moreover, they find new examples of non-compact and compact manifolds belonging to the class W.
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 4000928
zbMATH Keywords: generalized Heisenberg group
zbMATH Keywords: 7-dimensional manifolds
zbMATH Keywords: vector cross product
zbMATH Keywords: root systems
zbMATH Keywords: semisimple Lie algebras
Wikidata QID: Q115391471
MaRDI profile type: Publication
cites work: Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
cites work: Q5345512
cites work: Vector cross products
cites work: Construction and Properties of Some 6-Dimensional Almost Complex Manifolds
cites work: Systeme von Richtungsfeldern in Sphären und stetige Lösungen komplexer linearer Gleichungen
cites work: Riemannian manifolds with structure group \(G_ 2\)
cites work: Q4172188
cites work: Vector Cross Products on Manifolds
cites work: Weak holonomy groups
cites work: The sixteen classes of almost Hermitian manifolds and their linear invariants
cites work: Q3897665
cites work: Q5609479
full work available at URL: https://doi.org/10.1007/bf02844737
OpenAlex ID: W2025187197
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4000928