Invariant almost Hermitian structures on the maximal real flag manifold of type ${\mathcal{A}}_3$

Abstract

We study the Gray-Hervella classes of invariant almost Hermitian structures on the maximal real flag manifold of type ${\mathcal{A}}_3$. We first obtain an explicit parametrization of all invariant almost Hermitian structures and establish necessary and sufficient conditions for an invariant almost Hermitian structure to belong to each Gray-Hervella class. For each nonempty class, we give an explicit parametrization of the corresponding set of structures, describe it as a smooth manifold and determine its dimension.

arXiv comment21 pages