Einstein metrics via intrinsic or parallel torsion

Richard Cleyton*, Andrew Swann

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

36 Citations (Scopus)


The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts. The first consists of isolated examples: the Riemannian symmetric spaces. The second consists of geometries that can occur in continuous families: these include the Calabi-Yau structures and Joyce manifolds of string theory. One may ask how one can weaken the definitions and still obtain similar classifications. We present two closely related suggestions. The classifications for these give isolated examples that are isotropy irreducible spaces, and known families that are the nearly Kähler manifolds in dimension 6 and Gray's weak holonomy G2 structures in dimension 7.

Original languageEnglish
JournalMathematische Zeitschrift
Pages (from-to)513-528
Number of pages16
Publication statusPublished - 1 Jan 2004
Externally publishedYes


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