Super Kähler structures on the complex Abelian Lie supergroups

Meng-Kiat Chuah, Fabio Gavarini

Let $G$ be a real Abelian Lie supergroup, let $M$ be its complexification. We classify the $G$-invariant super Kähler forms on $M$. For the super Kähler forms with Hamiltonian acti…