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Non-Kähler complex
structures on $\mathbb{R}^4$
Antonio J Di Scala, Naohiko Kasuya and Daniele Zuddas |
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Geometry & Topology 21 (2017) 2461–2473
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Abstract |
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We construct the first examples of non-Kähler complex structures on . 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
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Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 57R40, 57R42
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References |
Publication
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
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Authors |
| Antonio J Di Scala | |
| Dipartimento di Scienze Matematiche
G L Lagrange Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy |
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| Naohiko Kasuya | |
| School of Social Informatics Aoyama Gakuin University 5-10-1 Fuchinobe Chuo-ku, Sagamihara Kanagawa 252-5258 Japan |
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| Daniele Zuddas | |
| School of Mathematics Korea Institute for Advanced Study 85 Hoegiro Dongdaemun-gu, Seoul 02455 South Korea |
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