Scalar curvatures of invariant almost Hermitian structures on flag manifolds with two and three isotropic summands

Abstract

In this paper we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or three irreducible components. We will provide a classification of such flag manifolds admitting Kähler like scalar curvature metric, that is, almost Hermitian structures (g , J ) satisfying s = 2s C where s is Riemannian scalar curvature and s C is the Chern scalar curvature.