Cleyton, Richard; Swann, Andrew Einstein metrics via intrinsic or parallel torsion. (English) Zbl 1069.53041 Math. Z. 247, No. 3, 513-528 (2004). This article is devoted to the classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection. The authors consider all \(G\)-structures on Riemannian manifolds with non-trivial intrinsic torsion. They impose various extra conditions on the \(G\)-structure and its intrinsic torsion to obtain Einstein metric. As a result, the classification of isolated examples that are isotropy irreducible spaces and the classification of known families that are nearly Kähler \(G\)-manifolds and Gray’s weak holonomy \(G_2\)-structures in dimension 7 are given. Reviewer: Valeriy A. Yumaguzhin (Opava) Cited in 4 ReviewsCited in 34 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C10 \(G\)-structures 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 53C29 Issues of holonomy in differential geometry Keywords:Riemannian manifold; Levi-Civita connection; Einstein metric; holonomy group; intrinsic torsion PDFBibTeX XMLCite \textit{R. Cleyton} and \textit{A. Swann}, Math. Z. 247, No. 3, 513--528 (2004; Zbl 1069.53041) Full Text: DOI arXiv