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Examples of Non-Kähler Solvmanifolds Admitting Hodge Decomposition

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Real and Complex Submanifolds

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 106))

Abstract

We consider some Hodge theoretical properties (formality, hard-Lefschetz property, E 1-degeneration of Frölicher spectral sequence, \(\partial \bar{\partial }\)-Lemma and their twisted versions) on non-Kähler symplectic and complex manifolds. It is known that if nilmanifolds satisfy formality, hard-Lefschetz property, or \(\partial \bar{\partial }\)-Lemma, then they are only tori. Hodge theory on solvmanifolds are more complicated. We give non-Kähler solvmanifolds satisfying these properties.

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Authors and Affiliations

  1. Department of Mathematics, Tokyo Institute of Technology, 1-12- 1 O-okayama, Meguro, Tokyo, 152-8551, Japan

    Hisashi Kasuya

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  1. Hisashi Kasuya
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Correspondence to Hisashi Kasuya .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Kyungpook National University, Daegu, Republic of Korea

    Young Jin Suh

  2. Department of Mathematics, King’s College London, London, UK

    Jürgen Berndt

  3. Department of Mathematics, Osaka City University, Osaka, Japan

    Yoshihiro Ohnita

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Republic of Korea

    Byung Hak Kim

  5. The Center for Geometry and its Applications, Pohang University of Science and Technology, Pohang, Republic of Korea

    Hyunjin Lee

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Kasuya, H. (2014). Examples of Non-Kähler Solvmanifolds Admitting Hodge Decomposition. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_20

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