A Proof Of A Formality On Generalized K(?)hler Manifolds

In this thesis, we review some properties of compact generalized Kahler manifolds, through which we mainly investigate the formality of compact generalized Kahler manifolds. Let (J1, J2) is a generalized Kahler structure on a compact manifold. If J1has holomorphically trival canon-ical bundle, we can obtain a correspondence between operators (?)L1 and (?)L1 onΩ·(L1) andδ+ andδ_onΩC·(M). Then using theδ+δ-_—lemma on compact generalized Kahler manifolds, we get (?)L1(?)L1—lemma on the special compact generalized Kahler manifolds. With the help of the (?)L1(?)L1—lemma, we prove a formality of generalized Kahler manifolds that is given by Gil R. Cavalcanti.