Vaisman Solvmanifolds and Relations with Other Geometric Structures

ADRIÁN ANDRADA; MARCOS ORIGLIA

ASIAN JOURNAL OF MATHEMATICS

INT PRESS BOSTON, INC

Año: 2019

1093-6106

We characterize unimodular solvable Lie algebras with Vaisman structures in termsof K¨ahler flat Lie algebras equipped with a suitable derivation. Using this characterization weobtain algebraic restrictions for the existence of Vaisman structures and we establish somerelations with other geometric notions, such as Sasakian, coK¨ahler and left-symmetric algebrastructures. Applying these results we construct families of Lie algebras and Lie groups admittinga Vaisman structure and we show the existence of lattices in some of these families, obtainingin this way many examples of new solvmanifolds equipped with invariant Vaisman structures.