no. 1
Complete real Kähler Euclidean hypersurfaces are cylinders
[Toute hypersurface Euclidienne réelle Kahlerienne et complète est un cylindre]
Florit, Luis A.1 ; Zheng, Fangyang2
1 IMPA: Estrada Dona Castorina 110 22460–320, Rio de Janeiro (Brazil)
2 Ohio State University Columbus, OH 43210 (USA) and Zhejiang University IMS Hanzhou (China)
Annales de l'Institut Fourier, Tome 57 (2007) no. 1, pp. 155-161.

Dans cet article nous montrons que toute hypersurface Kählerienne complète immergée dans un espace Euclidien M 2n ⊂ℝ 2n+1 est le produit d’une surface de ℝ 3 et d’un facteur Euclidien ℂ n-1 ≅ℝ 2n-2 .

In this note we show that any complete Kähler (immersed) Euclidean hypersurface M 2n ⊂ℝ 2n+1 must be the product of a surface in ℝ 3 with an Euclidean factor ℂ n-1 ≅ℝ 2n-2 .

DOI : 10.5802/aif.2254
Classification : 53C40, 53C55
Keywords: Kähler submanifolds, cylinders, splitting
Mot clés : Kähler hypersurface, cylindres, fendre
Florit, Luis A. 1 ; Zheng, Fangyang 2

1 IMPA: Estrada Dona Castorina 110 22460–320, Rio de Janeiro (Brazil)
2 Ohio State University Columbus, OH 43210 (USA) and Zhejiang University IMS Hanzhou (China) 
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     title = {Complete real {K\"ahler} {Euclidean} hypersurfaces are cylinders},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     zbl = {1119.53005},
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Florit, Luis A.; Zheng, Fangyang. Complete real Kähler Euclidean hypersurfaces are cylinders. Annales de l'Institut Fourier, Tome 57 (2007) no. 1, pp. 155-161. doi : 10.5802/aif.2254. http://www.numdam.org/articles/10.5802/aif.2254/

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