  A vector bundle E on a projective variety X is called finite if it satisfies
a nontrivial polynomial equation with integral coefficients. A theorem of Nori
implies that E is finite if and only if the pullback of E to some finite etale
Galois covering of X is trivial. We prove the same statement when X is a
compact complex manifold admitting a Gauduchon astheno-Kahler metric.
