Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with cite{ko6} now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension $ge 3.$
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机译：任何开放的黎曼曲面在任何尺寸为4的可定向黎曼流形中都有一个保形模型。精确地，我们将证明，在任何开放的黎曼曲面上，在一个预定的可定向4维黎曼流形中存在一个保形等效模型。现在，该结果与 cite {ko6}一起显示，一个开放的Riemann曲面允许在尺寸为 ge 3. $的任何Riemannian流形中采用共形模型。
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