Abstract: In the context of Hermitian geometry, the Hull–Strominger system is a system of non-linear PDEs on heterotic string theory.
We will begin the talk by introducing and giving a description of the geometry of cohomogeneity one manifolds. Then, we will look for solutions to the Hull–Strominger system in three dimensions in the cohomogeneity one setting.
This leads us to consider simply connected 3-dimensional balanced manifolds endowed with an invariant nowhere-vanishing holomorphic (3,0)-form which are of cohomogeneity one under the almost effective action of a connected Lie group G.
We show that one of such M would have to be compact and have a certain principal orbit type, up to G-equivariant diffeomorphism.