Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds

Abstract

In this paper, we study invariant almost Hermitian geometry on generalized flag manifolds. We will focus on providing examples of Kähler-like scalar curvature metric, that is, almost Hermitian structures (𝑔, 𝐽) satisfying 𝑠 =2𝑠C, where 𝑠 is Riemannian scalar curvature, and 𝑠C is the Chern scalar curvature.