Orientable hypersurfaces of Riemannian manifolds with Spin (7) structure
type: Item
instance of: scholarly article
title: Orientable hypersurfaces of Riemannian manifolds with Spin (7) structure
zbMATH Open document ID: 0904.53019
DOI: 10.1023/A:1006573220451
author: K. Appert
published in: Acta Mathematica Hungarica
publication date: 1998-11-22T00:00:00Z
review text: A Spin(7) structure is given by an \(8\)-dimensional Riemannian manifold \(\overline M\) and a nowhere vanishing \(4\)-form \(\overline \varphi\) on \(\overline M\). An orientable manifold \(M\) with a \(G_2\)-structure (the exceptional Lie group of authomorphisms of the Cayley numbers \(O\)) is \(7\)-dimensional, it has an induced Riemannian metric and there exists on it a nowhere vanishing \(3\)-form \(\varphi\). In the present paper \(\overline M\) is an ambient space of \(M\). Then the influence of \(\overline M\) on the type of the \(G_2\)-structure induced on \(M\) is studied and some types of these induced \(G_2\)-structures are characterized by means of the geometrical conditions satisfied by \(M\). One of these cases has been considered by A. Gray. Finally, some interesting examples are given.
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 57R15
zbMATH DE Number: 1225539
zbMATH Keywords: Spin(7) structure
zbMATH Keywords: hypersurface of Riemannian manifold
reviewed by: Lajos Tamássy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1225539