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

TL;DR

This paper classifies invariant almost Hermitian structures on certain flag manifolds with two or three isotropic summands that have scalar curvatures satisfying a specific proportionality condition.

Contribution

It provides a classification of flag manifolds with invariant almost Hermitian structures where the scalar curvature equals twice the Chern scalar curvature.

Findings

Identifies flag manifolds admitting Kähler-like scalar curvature metrics

Provides explicit conditions for the scalar curvature relation

Classifies structures based on isotropy representation decomposition

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 K\"ahler 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.