Nagoya Mathematical Journal

On the complement of Levi-flats in K\"{a}hler manifolds of dimension $\ge 3$

Takeo Ohsawa

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Applying the $L^2$ method of solving the $\bar{\partial}$-equation, it is shown that compact K\"{a}hler manifolds of dimension $\geq 3$ admit no Levi flat real analytic hypersurfaces whose complements are Stein.

Article information

Nagoya Math. J., Volume 185 (2007), 161-169.

First available in Project Euclid: 23 March 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32V40: Real submanifolds in complex manifolds
Secondary: 53C40: Global submanifolds [See also 53B25]


Ohsawa, Takeo. On the complement of Levi-flats in K\"{a}hler manifolds of dimension $\ge 3$. Nagoya Math. J. 185 (2007), 161--169.

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