On the real analytic Levi flat hypersurfaces in complex tori of dimension two

Kazuko Matsumoto[1]; Takeo Ohsawa[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)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 5, page 1525-1532
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Matsumoto, Kazuko, and Ohsawa, Takeo. "On the real analytic Levi flat hypersurfaces in complex tori of dimension two." Annales de l’institut Fourier 52.5 (2002): 1525-1532. <http://eudml.org/doc/116016>.

@article{Matsumoto2002,
abstract = {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.},
affiliation = {Osaka Women's University, Department of Applied Mathematics, Daisen-cho, Sakai 590-0035 (Japon); Nagoya University, Graduate School of Mathematics, Chikusa-ku, Nagoya 464-8602 (Japon)},
author = {Matsumoto, Kazuko, Ohsawa, Takeo},
journal = {Annales de l’institut Fourier},
keywords = {Levi flat; complex torus; real analytic Levi flat hypersurface; complex tori},
language = {eng},
number = {5},
pages = {1525-1532},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the real analytic Levi flat hypersurfaces in complex tori of dimension two},
url = {http://eudml.org/doc/116016},
volume = {52},
year = {2002},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 5
SP - 1525
EP - 1532
AB - 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.
LA - eng
KW - Levi flat; complex torus; real analytic Levi flat hypersurface; complex tori
UR - http://eudml.org/doc/116016
ER -

References

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  1. F. Docquier, H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann 140 (1960), 94-123 Zbl0095.28004MR148939
  2. A. Lins-Neto, A note on projective Levi-flats and minimal sets of algebraic functions, Ann. Inst. Fourier (1999), 1369-1385 Zbl0963.32022MR1703092
  3. D. Michel, Sur les ouverts pseudoconvexes des espaces homogènes, C. R. Acad. Sci. Paris, Sér. A 283 (1976), 779-782 Zbl0355.32019MR460726
  4. T. Ohsawa, Nonexistence of real analytic Levi flat hypersurfaces in ℙ 2 , Nagoya Math. J. 158 (2000), 95-98 Zbl1023.32026MR1766572
  5. Y.-T. Siu, Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension ≥ 3 , Ann. of Math. 151 (2000), 1217-1243 Zbl0980.53065MR1779568

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