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-K\"ahler SU(3)-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.
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