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 $\mathrm{SU}(\mathrm{n})$-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 $\mathrm{SU}(3)$-structures which are invariant under a cohomogeneity one action on simply connected six-manifolds.

20 pages. v4: case (b.1) has been corrected after an error was detected in equation (4.5) of v3. The statements of the theorems have been modified accordingly

References in corpus (2)

• Special Hermitian metrics on compact solvmanifolds
• Balanced Hermitian metrics from SU(2)-structures

Cited by in corpus (1)

• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds