On the real analytic Levi flat hypersurfaces in complex tori of dimension two  [ Sur les hypersurfaces analytiques réelles Levi-plates des tores complexes de dimension 2 ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1525-1532.

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.

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.

DOI : https://doi.org/10.5802/aif.1923
Classification : 32V40
Mots clés: Levi-plat, tore complexe
@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},
     pages = {1525--1532},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     doi = {10.5802/aif.1923},
     mrnumber = {1935555},
     zbl = {1031.32030},
     language = {en},
     url = {aif.centre-mersenne.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, Tome 52 (2002) no. 5, pp. 1525-1532. doi : 10.5802/aif.1923. https://aif.centre-mersenne.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 $\Bbb P^2$, 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 $\geq 3$, Ann. of Math., Tome 151 (2000) no. 3, pp. 1217-1243 | Article | | MR 1779568 | Zbl 0980.53065