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, of left-invariant metrics on a $6$-dimensional Lie group $H$, such that its Lie algebra $\mathfrak{h}$ admits a complex structure and has first Betti number equal to four. We also investigate which of these metrics are Hermitian and classify the corresponding complex structures.

37 pages

Cited by in corpus (1)

• On the moduli spaces of left invariant metrics on cotangent bundle of Heisenberg group