标题： Oeljeklaus-Toma流形上的多个复结构 显示英文标题

标题： Several complex structures on the Oeljeklaus-Toma manifolds

摘要： 我们研究Oeljeklaus-Toma流形上的复结构。 Oeljeklaus-Toma流形是通过数域的复嵌入定义的。 通过将这些嵌入替换为它们的共轭，可以得到具有相同基础微分结构的其他流形。 在本文中，我们给出了这些流形为全纯同构时的代数描述。 作为简单应用，我们得到了维数为$2t+1$的紧致非凯勒流形，它们允许$2^t$个不同的刚性复结构。 显示英文摘要

摘要： We investigate complex structures on the Oeljeklaus-Toma manifolds. The Oeljeklaus-Toma manifolds are defined using complex embeddings of number fields. By replacing these embeddings with their conjugates, one obtains other manifolds that share the same underlying differential structure. In this paper, we give an algebraic description of when such manifolds are biholomorphic. As a simple application, we obtain compact non-K\"{a}hler manifolds of dimension $2t+1$ that admit $2^t$ different rigid complex structures.