Futaki invariant on Hopf manifolds

The Futaki invariant is a fundamental tool in Kähler geometry representing, for instance, an obstruction to the existence of Kähler–Einstein metrics. Recently, it was generalized to any compact complex manifold by Futaki, Hattori, and Ornea [Manuscripta Math. 140 (2013), pp. 1–12]. In this paper, we prove that it vanishes on all Hopf manifolds, providing a partial answer to a question raised by Ornea and Verbitsky [Progress in Mathematics 354 (2024)].