Vaisman solvmanifolds and relations with other geometric structures
Abstract
We characterize unimodular solvable Lie algebras with Vaisman structures in terms of K\"ahler 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, coK\"ahler 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.
Cite
@article{arxiv.1709.01567,
title = {Vaisman solvmanifolds and relations with other geometric structures},
author = {Adrián Andrada and Marcos Origlia},
journal= {arXiv preprint arXiv:1709.01567},
year = {2020}
}
Comments
Minor modifications added to the first version. Accepted for publication in The Asian Journal of Mathematics (AJM)