Hodge Theoretic Results for Nearly Kähler Manifolds

A nearly Kähler six-manifold admits a compatible SU(3)-structure. Verbitsky utilised this SU(3)-structure to obtain a generalisation of the Kähler identities, which he used to prove a Hodge decomposition analogous to the Kähler case. We extend these identities and the Hodge decomposition to nearly Kähler manifolds in arbitrary dimensions. This is joint work with Spiro Karigiannis, Lucía Martín-Merchán, and Aleksandar Milivojević.