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Compact complex non-Kähler manifolds associated with totally real reciprocal units

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Using the theory of totally real number fields we construct a new class of compact complex non-Kähler manifolds in every even complex dimension and study their analytic and geometric properties.

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Correspondence to Christian Miebach.

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Dedicated to Alan T. Huckleberry on the occasion of his 80th birthday.

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The authors would like to thank Professor A. Dubickas for helping kindly in number theoretical questions in particular for giving Lemma 2.2 with a proof. The authors are grateful for invitations to the “Institut de Mathématiques de Marseille (I2M)” and “Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville (LMPA)”, where part of this research was carried out.

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Miebach, C., Oeljeklaus, K. Compact complex non-Kähler manifolds associated with totally real reciprocal units. Math. Z. 301, 2747–2760 (2022).

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