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

We construct the first examples of non-Kähler complex structures on 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.

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achiral Lefschetz fibration, non-Kähler complex manifold, nonstandard complex Euclidean space
Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 57R40, 57R42
Received: 23 March 2016
Revised: 28 April 2016
Accepted: 24 September 2016
Published: 19 May 2017
Proposed: Yasha Eliashberg
Seconded: Bruce Kleiner, András I. Stipsicz
Antonio J Di Scala
Dipartimento di Scienze Matematiche G L Lagrange
Politecnico di Torino
Corso Duca degli Abruzzi 24
10129 Torino
Naohiko Kasuya
School of Social Informatics
Aoyama Gakuin University
5-10-1 Fuchinobe
Chuo-ku, Sagamihara
Kanagawa 252-5258
Daniele Zuddas
School of Mathematics
Korea Institute for Advanced Study
85 Hoegiro
Dongdaemun-gu, Seoul 02455
South Korea