Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds

ADRIÁN ANDRADA; ALEJANDRO TOLCACHIER

ANNALI DI MATEMATICA PURA ED APPLICATA

SPRINGER HEIDELBERG

Lugar: HEIDELBERG; Año: 2023

0373-3114

An almost abelian Lie group is a solvable Lie group with a codimension one normal abelian subgroup. We characterize almost Hermitian structures on almost abelian Lie groups where the almost complex structure is harmonic with respect to the Hermitian metric. Also, weadapt the Gray–Hervella classification of almost Hermitian structures to the family of almost abelian Lie groups. We provide several examples of harmonic almost complex structures in different Gray–Hervella classes on some associated compact almost abelian solvmanifolds.