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.
@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}, 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, Tome 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] Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann, Volume 140 (1960), pp. 94-123 | Article | EuDML 160766 | MR 148939 | Zbl 0095.28004
[LN] A note on projective Levi-flats and minimal sets of algebraic functions, Ann. Inst. Fourier (1999), pp. 1369-1385 | Article | EuDML 75385 | Numdam | MR 1703092 | Zbl 0963.32022
[M] Sur les ouverts pseudoconvexes des espaces homogènes, C. R. Acad. Sci. Paris, Sér. A, Volume 283 (1976), pp. 779-782 | MR 460726 | Zbl 0355.32019
[O] Nonexistence of real analytic Levi flat hypersurfaces in , Nagoya Math. J., Volume 158 (2000), pp. 95-98 | MR 1766572 | Zbl 1023.32026
[S] Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension , Ann. of Math., Volume 151 (2000) no. 3, pp. 1217-1243 | Article | EuDML 121614 | MR 1779568 | Zbl 0980.53065