Geodesic
Non-Kähler complex structures on ℝ4
Di Scala, Antonio1 ; Kasuya, Naohiko2 ; Zuddas, Daniele3
1 Dipartimento di Scienze Matematiche G L Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 School of Social Informatics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
3 School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, South Korea
Geometry & topology, Tome 21 (2017) no. 4, pp. 2461-2473.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We construct the first examples of non-Kähler complex structures on ℝ4. 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.

DOI : 10.2140/gt.2017.21.2461
Classification : 32Q15, 57R40, 57R42
Keywords: achiral Lefschetz fibration, non-Kähler complex manifold, nonstandard complex Euclidean space

Di Scala, Antonio 1 ; Kasuya, Naohiko 2 ; Zuddas, Daniele 3

1 Dipartimento di Scienze Matematiche G L Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2 School of Social Informatics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan
3 School of Mathematics, Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul 02455, South Korea 
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     title = {Non-K\"ahler complex structures on {\ensuremath{\mathbb{R}}4}},
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Di Scala, Antonio; Kasuya, Naohiko; Zuddas, Daniele. Non-Kähler complex structures on ℝ4. Geometry & topology, Tome 21 (2017) no. 4, pp. 2461-2473. doi : 10.2140/gt.2017.21.2461. http://geodesic.mathdoc.fr/articles/10.2140/gt.2017.21.2461/

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