Examples of relatively ding unstable calabi dream manifolds

The Mabuchi constant is a holomorphic invariant of Fano manifolds, which obstructs the existence of Mabuchi's generalized Kahler-Einstein metrics and relative Ding semistability. In this study, we give a formula for the Mabuchi constant of produtcs of Fano manifolds. As an application, we present examples of Fano manifolds which admit Calabi's extremal Kahler metrics in every Kahler class, but are relatively Ding unstable.