We study a supersymmetry-preserving solution-generating method in heterotic supergravity. In particular, we use this method to construct one-parameter non-Kähler deformations of Calabi–Yau manifolds with a $U(1)$ isometry, in which the complex structure remains invariant. We explain how to obtain corresponding solutions to heterotic string theory, up to first order in $\alpha'$, by a modified form of the standard embedding. In the course of the paper we also show that Abelian heterotic supergravity embeds into type II supergravity, and note that the solution-generating method in this context is related to a dipole-type deformation when there is a field theory dual.
"Non-Kähler heterotic rotations." Adv. Theor. Math. Phys. 15 (1) 131 - 174, January 2011.