On the existence of balanced metrics on six-manifolds of cohomogeneity one

Abstract

We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced SU(n)-structures. Such structures are of interest for both Hermitian geometry and string theory, since they provide the ideal setting for the Hull–Strominger system. In this paper, we provide a non-existence result for balanced non-Kähler text {SU}(3)-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.