In this paper we obtain a stability theorem of generalized Kähler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kähler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kähler manifolds which admits deformations to generalized complex manifolds and obtain non-trivial generalized Kähler structures on Fano surfaces and toric Kähler manifolds. In particular, we show that every nonzero holomorphic Poisson structure on a Kähler manifold induces deformations of non-trivial generalized Kähler structures.
"Deformations of generalized complex generalized Kahler structures." J. Differential Geom. 84 (3) 525 - 560, March 2010. https://doi.org/10.4310/jdg/1279114300