The moduli space of left-invariant metrics of a class of six-dimensional nilpotent Lie groups

Abstract

In this paper we determine the moduli space, up to isometric automorphism, ofleft-invariant metrics on a 6-dimensional Lie group H, such that its Liealgebra h admits a complex structure and has first Betti numberequal to four. We also investigate which of these metrics are Hermitian andclassify the corresponding complex structures.