Um estudo sobre estruturas Kähler e aproximadamente Kähler em variedades flag: respondendo à conjectura de Wolf e Gray

Abstract

In this work, we study conditions for which a flag manifold having invariant structures, admits a nearly-Kähler structure that is not Kähler. This is a partial answer to a conjecture by Wolf and Gray, that was studied in an article by Luiz A. B. San Martin and Rita de Cássia de J. Silva. Moreover, we create a sequence of results that can be utilized as a study guide to those interested in studying the geometry of flag manifolds, as the literature is scarce in introductory resources to this topic.