This is a continuation of our study on homogeneous locally conformally K ̈ahler and Sasaki mani-folds. In a recent work [2], applying the technique of modification we have determinedall homogeneousSasaki and Vaisman manifolds of unimodular Lie groups, up tomodifications. In this paper we de-termine all such modifications explicitly for the case of Liegroups, obtaining a complete classificationof unimodular Sasaki and Vaisman Lie groups. Furthermore, we determine the biholomorphism typeof a simply connected unimodular Vaisman Lie group of each type.
In our previous work (Alekseevsky et al., Nagoya Math J 8:1–14, 2019), applying the technique of modification, all homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups have been classified, up to modifications. In this paper we determine all such modifications explicitly for the case of Lie groups, obtaining a complete classification of unimodular Sasaki and Vaisman Lie groups. Furthermore, we determine the biholomorphism type of a simply connected unimodular Vaisman Lie group of each type.