Einstein metrics via intrinsic or parallel torsion. (English) Zbl 1069.53041

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.


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
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