Vaisman solvmanifolds and relations with other geometric structures

2017/09/05 by Adrián Andrada, Andrada, Adrián, Marcos Origlia +1 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1709.01567

Minor modifications added to the first version. Accepted for publication in The Asian Journal of Mathematics (AJM)

arxiv created 2020/04/02 · arxiv updated 2020/04/06

Abstract

We characterize unimodular solvable Lie algebras with Vaisman structures in terms of Kähler 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, coKähler 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.

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