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Compact CR-solvmanifolds as Kähler obstructions

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Abstract

We give a precise characterization for when a compact CR-solvmanifold is CR-embeddable in a complex Kähler manifold. Equivalently this gives a non-Kähler criterion for complex manifolds containing CR-solvmanifolds not satisfying these conditions. This paper is the natural continuation of Oeljeklaus and Richthofer [J Differ Geom 27(3):399–421, 1988] and Gilligan et al. [Can J Math 41(1):163–177, 1989].

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Regina, 3737 Wascana Boulevard, Regina, S4S 0A2, Canada

    Bruce Gilligan

  2. LATP-UMR(CNRS) 6632, CMI-Université d’Aix-Marseille I, 39, rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Karl Oeljeklaus

Authors
  1. Bruce Gilligan
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  2. Karl Oeljeklaus
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Correspondence to Bruce Gilligan.

Additional information

This work was partially done during a visit of the first author at the LATP at the Université de Provence in June 2008 and of the second author at the University of Regina in October–November 2008. We would like to thank the respective institutions for their hospitality and financial support. This work was also partially supported by an NSERC Discovery Grant. The authors also thank the referee for suggestions that improved the presentation of the paper.

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Gilligan, B., Oeljeklaus, K. Compact CR-solvmanifolds as Kähler obstructions. Math. Z. 269, 179–191 (2011). https://doi.org/10.1007/s00209-010-0721-6

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  • DOI: https://doi.org/10.1007/s00209-010-0721-6

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