Isometry groups of six-dimensional nilmanifolds

Abstract

We determine the 6-dimensional nilpotent metric Lie algebras such that the Lie algebra {mathfrak {n}} has a descending series of ideals invariant under all automorphisms of {mathfrak {n}} and the dimension of the consecutive members of the series decreases by one. We call them metric Lie algebras having a framing determined by ideals. We classify the isometry equivalence classes and determine the isometry groups of connected and simply connected Riemannian nilmanifolds on 6-dimensional nilpotent Lie groups having a Lie algebra {mathfrak {n}} as their Lie algebra.