Classification des varietes approximativement kahleriennes homogenes

TL;DR

This paper proves a conjecture linking nearly Kahler structures on homogeneous manifolds to 3-symmetric spaces, classifying them in dimension 6 and extending results to higher dimensions.

Contribution

It confirms Gray & Wolf's conjecture and provides a classification of nearly Kahler homogeneous manifolds, advancing understanding of their geometric structure.

Findings

Nearly Kahler homogeneous manifolds are 3-symmetric in dimension 6

The conjecture holds in higher dimensions based on previous results

Classification results for nearly Kahler structures are established

Abstract

We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions.