Abstract
We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kahler flat Lie algebras equipped with a suitable derivation. Using this characterization we obtain algebraic restrictions for the existence of Vaisman structures and we establish some relations with other geometric notions, such as Sasakian, coKahler and left-symmetric algebra structures. Applying these results we construct families of Lie algebras and Lie groups admitting a Vaisman structure and we show the existence of lattices in some of these families, obtaining in this way many examples of new solvmanifolds equipped with invariant Vaisman structures.
Original language | English |
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Pages (from-to) | 117-146 |
Number of pages | 30 |
Journal | Asian Journal of Mathematics |
Volume | 24 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Lattice
- Locally conformally kähler structure
- Solvable lie group
- Solvmanifold
- Vaisman structure