On the real analytic Levi flat hypersurfaces in complex tori of dimension two
Annales de l'Institut Fourier, Volume 52 (2002) no. 5, p. 1525-1532

We compute the Levi form of the logarithm of the distance function for real hypersurfaces in two dimensional complex tori, and discuss the characterization of Levi flat hypersurfaces there.

Nous calculons la forme de Levi du logarithme de la fonction de distance pour les hypersurfaces réelles dans un tore complexe de dimension 2 et discutons de la caractérisation des hypersurfaces Levi-plates.

DOI : https://doi.org/10.5802/aif.1923
Classification:  32V40
Keywords: Levi flat, complex torus
@article{AIF_2002__52_5_1525_0,
     author = {Matsumoto, Kazuko and Ohsawa, Takeo},
     title = {On the real analytic Levi flat hypersurfaces in complex tori of dimension two},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     pages = {1525-1532},
     doi = {10.5802/aif.1923},
     zbl = {1031.32030},
     mrnumber = {1935555},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2002__52_5_1525_0}
}
Matsumoto, Kazuko; Ohsawa, Takeo. On the real analytic Levi flat hypersurfaces in complex tori of dimension two. Annales de l'Institut Fourier, Volume 52 (2002) no. 5, pp. 1525-1532. doi : 10.5802/aif.1923. http://www.numdam.org/item/AIF_2002__52_5_1525_0/

[D-G] F. Docquier; H. Grauert Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann, Tome 140 (1960), pp. 94-123 | Article | MR 148939 | Zbl 0095.28004

[LN] A. Lins-Neto A note on projective Levi-flats and minimal sets of algebraic functions, Ann. Inst. Fourier (1999), pp. 1369-1385 | Article | Numdam | MR 1703092 | Zbl 0963.32022

[M] D. Michel Sur les ouverts pseudoconvexes des espaces homogènes, C. R. Acad. Sci. Paris, Sér. A, Tome 283 (1976), pp. 779-782 | MR 460726 | Zbl 0355.32019

[O] T. Ohsawa Nonexistence of real analytic Levi flat hypersurfaces in 2 , Nagoya Math. J., Tome 158 (2000), pp. 95-98 | MR 1766572 | Zbl 1023.32026

[S] Y.-T. Siu Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension 3, Ann. of Math., Tome 151 (2000) no. 3, pp. 1217-1243 | Article | MR 1779568 | Zbl 0980.53065