A Vaisman manifold is a special kind of locally conformally Kähler manifold, which is closely related to a Sasaki manifold. In this paper, we show a basic structure theorem of simply connected homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups, up to holomorphic isometry. For the case of unimodular Lie groups, we obtain a complete classification of simply connected Sasaki and Vaisman unimodular Lie groups, up to modification.

中文翻译：

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单模李群的齐次 SASAKI 和 VAISMAN 流形

Vaisman 流形是一种特殊的局部共形 Kähler 流形，它与 Sasaki 流形密切相关。在本文中，我们展示了单模李群的简单连接齐次 Sasaki 和 Vaisman 流形的基本结构定理，直至全纯等距。对于单模李群的情况，我们获得了简单连通的 Sasaki 和 Vaisman 单模李群的完整分类，直至修改。