Unimodular Sasaki and Vaisman Lie groups
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Publication:6338073
DOI10.1007/S00209-023-03233-6arXiv2004.02112MaRDI QIDQ6338073
Vicente Cortés, Keizo Hasegawa
Publication date: 5 April 2020
Abstract: This is a continuation of our study on homogeneous locally conformally Kaehler and Sasaki manifolds. In a recent work, applying the technique of modification we have determined all homogeneous Sasaki and Vaisman manifolds of unimodular Lie groups, 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.
Global theory of symplectic and contact manifolds (53D35) Local differential geometry of Hermitian and Kählerian structures (53B35) Homogeneous complex manifolds (32M10)
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