On locally homogeneous \(G\)-structures
type: Item
instance of: scholarly article
title: On locally homogeneous \(G\)-structures
zbMATH Open document ID: 0943.53019
DOI: 10.1023/A:1005007920878
published in: Geometriae Dedicata
publication date: 1999-01-17T00:00:00Z
review text: A theorem of \textit{I. M. Singer} [Commun. Pure Appl. Math. 13, 685-697 (1960; Zbl 0171.42003)] states that a Riemannian manifold \((M,g)\) is locally homogeneous if and only if it is infinitesimally homogeneous, that is, for each pair of points \(p,q\in M\) there exists an isometry \(F\) between \(T_pM\) and \(T_qM\) which preserves the covariant derivatives of the Riemann curvature tensor up to order \(k_M+ 1\), for an integer \(k_M\leq n(n- 1)/2- 1\), \(n= \dim M\). In the present paper, the author extends the notion of infinitesimal homogeneity to invariant connections on \(G\)-structures and proves a generalization of Singer's theorem. The general results are then applied to discuss the cases of conformal and Weyl structures.
reviewed by: Lorenzo Nicolodi
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 53B05
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1240982
zbMATH Keywords: \(G\)-structure
zbMATH Keywords: conformal structure
zbMATH Keywords: Weyl structure
zbMATH Keywords: infinitesimally homogeneous
author: Barbara Opozda
MaRDI profile type: Publication
full work available at URL: a:1005007920878
OpenAlex ID: W164939356
description: scientific article; zbMATH DE number 1240982