Fermionic T-duality in massive type IIA supergravity on

Fermionic T-duality transformation is studied for supersymmetric solutions of massive type IIA supergravity with the metric $$AdS_{10-k} \times M_k$$ for $$k=3$$ and 5. We derive the Killing spinors of these backgrounds and use them as input for the fermionic T-duality transformation. The resulting dual solutions form a large family of supersymmetric deformations of the original solutions by complex valued RR fluxes. We observe that the Romans mass parameter does not change under fermionic T-duaity, and prove its invariance in the $$k=3$$ case