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.

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: 10.5802/aif.1923
Classification: 32V40
Keywords: Levi flat, complex torus
Mot clés : Levi-plat, tore complexe
Matsumoto, Kazuko 1; Ohsawa, Takeo 2

1 Osaka Women's University, Department of Applied Mathematics, Daisen-cho, Sakai 590-0035 (Japon)
2 Nagoya University, Graduate School of Mathematics, Chikusa-ku, Nagoya 464-8602 (Japon)
@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{\textquoteright}institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     doi = {10.5802/aif.1923},
     zbl = {1031.32030},
     mrnumber = {1935555},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1923/}
}
TY  - JOUR
AU  - Matsumoto, Kazuko
AU  - Ohsawa, Takeo
TI  - On the real analytic Levi flat hypersurfaces in complex tori of dimension two
JO  - Annales de l'Institut Fourier
PY  - 2002
SP  - 1525
EP  - 1532
VL  - 52
IS  - 5
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1923/
DO  - 10.5802/aif.1923
LA  - en
ID  - AIF_2002__52_5_1525_0
ER  - 
%0 Journal Article
%A Matsumoto, Kazuko
%A Ohsawa, Takeo
%T On the real analytic Levi flat hypersurfaces in complex tori of dimension two
%J Annales de l'Institut Fourier
%D 2002
%P 1525-1532
%V 52
%N 5
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1923/
%R 10.5802/aif.1923
%G en
%F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1923/

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

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

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

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

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

Cited by Sources: