On the displacement rigidity of Levi flat hypersurfaces -- the case of boundaries of disc bundles over compact Riemann surfaces

DOI10.2977/prims/1199403813zbMath1141.53040arXivmath/0511108OpenAlexW2109420994MaRDI QIDQ2467699

Takeo Ohsawa, Klas Diederich

Publication date: 28 January 2008

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511108

zbMATH Keywords

rigiditycompact Riemann surfacesdisc bundlesLevi flats

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Rigidity results (53C24) Coverings of curves, fundamental group (14H30) CR manifolds as boundaries of domains (32V15) Holomorphic bundles and generalizations (32L05) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Deformations of fiber bundles (32G08) Deformations of special (e.g., CR) structures (32G07)

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Cites Work

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• A smooth pseudoconvex domain without pseudoconvex exhaustion
• The Hartogs-type extension theorem for meromophic mappings into compact Kähler manifolds
• Harmonic mappings and disc bundles over compact Kähler manifolds
• Biholomorphic domains with inequivalent boundaries
• A Levi problem on two-dimensional complex manifolds
• On univalent harmonic maps between surfaces
• Minimal algebraic foliations in \(\mathbb{C}\mathbb{P}(n)\)
• Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension \(\geq 3\)
• A Stein domain with smooth boundary which has a product structure
• \(\bar\partial\)-regularity for weakly pseudoconvex domains in compact Hermitian symmetric spaces with respect to invariant metrics
• On the real analytic Levi flat hypersurfaces in complex tori of dimension two
• On the Levi-flats in complex tori of dimension two
• Domaines pseudoconvexes infinis et la métrique riemannienne dans un espace projectif
• Harmonic Mappings of Riemannian Manifolds