Abstract
For algebraic number fields K with s>0 real and 2t>0 complex embeddings and “admissible” subgroups U of the multiplicative group of integer units of K we construct and investigate certain (s+t)-dimensional compact complex manifolds X(K,U). We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when t=1. In particular we disprove a conjecture of I. Vaisman.
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