Volume 21, issue 4 (2017)

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Non-Kähler complex structures on $\mathbb{R}^4$

Antonio J Di Scala, Naohiko Kasuya and Daniele Zuddas

Geometry & Topology 21 (2017) 2461–2473
Abstract

We construct the first examples of non-Kähler complex structures on ${ℝ}^{4}$. These complex surfaces have some analogies with the complex structures constructed in the early fifties by Calabi and Eckmann on the products of two odd-dimensional spheres. However, our construction is quite different from that of Calabi and Eckmann.

Keywords
achiral Lefschetz fibration, non-Kähler complex manifold, nonstandard complex Euclidean space
Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 57R40, 57R42