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Balanced manifolds and SKT metrics

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Abstract

The equality between the balanced and the Gauduchon cones is discussed in several situations. In particular, it is shown that equality does not hold on many twistor spaces, and it holds on Moishezon manifolds. Moreover, it is proved that a SKT manifold of dimension three on which the balanced cone equals the Gauduchon cone is in fact Kähler.

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Acknowledgements

The second author acknowledges the support of the Simons Foundation’s “Collaboration Grant for Mathematicians”, while the third author was supported by the NSF grant DMS-1309029.

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Author notes

  1. Ionuţ Chiose and Ioana Şuvaina are contributing equal to this work.

Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Ionuţ Chiose

  2. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN, 37240, USA

    Rareş Răsdeaconu & Ioana Şuvaina

Authors
  1. Ionuţ Chiose
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  2. Rareş Răsdeaconu
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  3. Ioana Şuvaina
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Correspondence to Rareş Răsdeaconu.

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Chiose, I., Răsdeaconu, R. & Şuvaina, I. Balanced manifolds and SKT metrics. Annali di Matematica 201, 2505–2517 (2022). https://doi.org/10.1007/s10231-022-01207-9

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