Vaisman solvmanifolds and relations with other geometric structures

A. Andrada, M. Origlia

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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 languageEnglish
Pages (from-to)117-146
Number of pages30
JournalAsian Journal of Mathematics
Issue number1
Publication statusPublished - 2020


  • Lattice
  • Locally conformally kähler structure
  • Solvable lie group
  • Solvmanifold
  • Vaisman structure

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