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Conformally parallel G 2 structures on a class of solvmanifolds

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Abstract

Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G 2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G 2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the corresponding non-homogeneous Ricci-flat metrics with holonomy contained in G 2. In the process we also find a new metric with exceptional holonomy.

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Authors and Affiliations

  1. Institut für Mathematik der Humboldt-Universität, Unter den Linden 6, 10099, Berlin, Germany

    Simon G. Chiossi

  2. Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123, Torino, Italy

    Anna Fino

Authors
  1. Simon G. Chiossi
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  2. Anna Fino
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Correspondence to Anna Fino.

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Received: 20 September

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Chiossi, S., Fino, A. Conformally parallel G 2 structures on a class of solvmanifolds. Math. Z. 252, 825–848 (2006). https://doi.org/10.1007/s00209-005-0885-7

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