Bochner formulae for orthogonal \(G\)-structures on compact manifolds.
type: Item
instance of: scholarly article
title: Bochner formulae for orthogonal \(G\)-structures on compact manifolds.
zbMATH Open document ID: 1036.53015
DOI: 10.1016/S0926-2245(01)00059-6
author: Gil Bor
author: Luis Hernández Lamoneda
published in: Differential Geometry and its Applications
publication date: 2002-08-14T00:00:00Z
review text: In this article, a general approach is developed to obtain an obstruction to the existence of reductions of an \(\text{O}(n)\)-structure on a compact manifold to a subgroup \(G\subset \text{O}(n)\). This obstruction is given in the form of an integral formula connecting the \(G\)-irreducible components of the intrinsic torsion tensor of the \(G\)-structure with \(G\)-invariants of the curvature tensor of the associated Riemannian metric. The approach is illustrated for the groups \(\text{U}_n\), \(n\geq 2\); \(\text{SU}_n\), \(n\geq 3\); \(G_2\) and \(\text{Spin}_7\).
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1780857
zbMATH Keywords: obstruction
zbMATH Keywords: reductions of a \(\text{O}(n)\)-structure
zbMATH Keywords: irreducible components
zbMATH Keywords: intrinsic torsion
reviewed by: Valeriy Yumaguzhin
MaRDI profile type: Publication
Wikidata QID: Q115338250
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full work available at URL: s0926-2245(01)00059-6
OpenAlex ID: W1972740660
description: scientific article; zbMATH DE number 1780857