Isometry groups of six-dimensional nilmanifolds

Abstract

We determine the 6-dimensional nilpotent metric Lie algebras such that the Lie algebra n has a descending series of ideals invariant under all automorphisms of 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 n as their Lie algebra.Mathematics Subject Classification (2010). Primary 53C30; Secondary 57M60, 17B30, 22E25.