Examples of relatively Ding unstable Calabi dream manifolds

Abstract

The Mabuchi constant is a holomorphic invariant of Fano manifolds, which obstructs the existence of Mabuchi’s generalized Kähler-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 Kähler metrics in every Kähler class, but are relatively Ding unstable.