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Einstein metrics via intrinsic or parallel torsion

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Abstract.

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Richard Cleyton & Andrew Swann

  2. Department of Mathematics, University of California, Riverside, CA 92507, USA

    Richard Cleyton

Authors
  1. Richard Cleyton
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  2. Andrew Swann
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Correspondence to Richard Cleyton.

Additional information

Mathematics Subject Classification (2000): 53C10, 17B10, 53C25, 53C29

in final form: 11 June 2003

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Cleyton, R., Swann, A. Einstein metrics via intrinsic or parallel torsion. Math. Z. 247, 513–528 (2004). https://doi.org/10.1007/s00209-003-0616-x

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  • DOI: https://doi.org/10.1007/s00209-003-0616-x

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