For a holomorphic one-form \({\xi }\) on a weakly 1-complete manifold X with certain properties, we will discuss the connectivity of the pair \((\hat{X},F^{-1}(z))\), where \(\pi :\hat{X} \rightarrow X\) is a covering map and F is a holomorphic function on \(\hat{X}\) such that \(dF=\pi ^*{\xi }\). We will also discuss the criteria about when such a manifold X admits a proper holomorphic mapping onto a Riemann surface.

中文翻译：

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弱1-完全流形上全纯单型的Lefschetz定理

对于具有某些性质的弱1完全流形X上的全纯单形式\（{\ xi} \），我们将讨论对\（（\ hat {X}，F ^ {-1}（ z））\），其中\（\ pi：\ hat {X} \ rightarrow X \）是覆盖图，F是\（\ hat {X} \）上的全纯函数，使得\（dF = \ pi ^ * {\ xi} \）。我们还将讨论有关何时流形X允许在Riemann曲面上适当的全纯映射的标准。