The Tanno Theorem for Kählerian metrics with arbitrary signature

Considering a non-constant smooth solution f   of the Tanno equation on a closed, connected Kähler manifold (M,g,J)(M,g,J) with positively definite metric g  , Tanno showed that the manifold can be finitely covered by (CP(n),const⋅gFubini–Study,Jstandard)(CP(n),const⋅gFubini–Study,Jstandard). The goal of this paper is to give a proof of Tannos Theorem for Kähler metrics with arbitrary signature.