On certain locally homogeneous Clifford manifolds
type: Item
instance of: scholarly article
title: On certain locally homogeneous Clifford manifolds
zbMATH Open document ID: 0832.53039
DOI: 10.1007/BF00773661
author: M. L. Barberis
author: Isabel Dotti Miatello
author: R. J. Miatello
published in: Annals of Global Analysis and Geometry
publication date: 1995-09-04T00:00:00Z
review text: A Clifford structure of order \(m\) on a connected differentiable manifold \(M\) is a family of \(m\) anticommuting complex structures generating a subalgebra of dimension 2 of \(\text{End} (T(M))\). In this paper, the authors investigate the existence of locally invariant Clifford structures of order \(m \geq 2\) on a class of locally homogeneous manifolds. They study the case of solvable extensions of \(H\)-type groups, showing in particular that the solvable Lie groups corresponding to the symmetric spaces of negative curvature carry invariant Clifford structures of order \(m \geq 2\). They also show that for each \(m\) and any finite group \(F\), there is a compact flat manifold with holonomy group \(F\) and carrying a Clifford structure of order \(m\).
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 792880
zbMATH Keywords: Clifford structures
zbMATH Keywords: hypercomplex structures
zbMATH Keywords: \(H\)-type groups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00773661
OpenAlex ID: W2035630344
description: scientific article; zbMATH DE number 792880