In this paper we show if E is a totally real Galois extension of \({{\mathbb {Q}}}\) of degree s then there is a cubic extension K of E with signature (s, s) such that in the group of units of K there are s multiplicatively independent positive units with the following property: if \(\alpha \) is any of those s units then there are two conjugates of \(\alpha \) over \({{\mathbb {Q}}}\) which are complex conjugate numbers lying on the circle \(|z|=\alpha ^{-1/2}\). In particular, our result combined with a recent result of Otiman implies that the corresponding Oeljeklaus–Toma manifold X(K, U) admits a pluriclosed metric.

在本文中，我们证明如果E是度为s的\（{{\ mathbb {Q}}} \）的完全实在的Galois扩展，则存在具有签名（s，  s）的E的三次扩展K，使得在的单位组ķ有小号乘法与下列属性独立的正单元：如果\（\阿尔法\）是任何那些的小号单元则有两个共轭物\（\阿尔法\）超过\（{{\ mathbb { Q}}} \）是位于圆\（| z | = \ alpha ^ {-1/2} \）上的复共轭数。特别是，我们的结果与Otiman的最新结果相结合，意味着相应的Oeljeklaus-Toma流形X（K，  U）接受了多封闭度量。