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- W2094034258 abstract "This is the so-called Hartogs-type extension problem. If U = An for any f with values in our X and any initial (nonempty!) U then one says that the Hartogs-type extension theorem holds for meromorphic mappings into this X. For X = C, i.e., for holomorphic functions, the Hartogs-type extension theorem was proved by F. Hartogs in [Ha]. If X = CiP1, i.e., for meromorphic functions, the result is due to E. Levi, see [Lv]. Since then the Hartogs-type extension theorem has been proved in at least two essentially more general cases than just holomorphic or meromorphic functions. Namely, for mappings into Kahler manifolds and into manifolds carrying complete Hermitian metrics of nonpositive holomorphic sectional curvature, see [Gr], [Iv-3], [Si-2], [Sh-1]. The goal of this paper is to initiate the systematic study of extension properties of meromorphic mappings with values in non-Kaihler complex manifolds. Let h be some Hermitian metric on a complex manifold X and let wh be the associated (1,1)-form. We call wh (and h itself) pluriclosed or ddC-closed if ddCwh = 0. In the sequel we shall not distinguish between Hermitian metrics and their associated forms. The latter we shall call simply metric forms." @default.
- W2094034258 created "2016-06-24" @default.
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- W2094034258 date "2004-11-01" @default.
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- W2094034258 title "Extension properties of meromorphic mappings with values in non-Kähler complex manifolds" @default.
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