Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds

TL;DR

This paper investigates invariant almost Hermitian structures on generalized flag manifolds, focusing on examples where the Riemannian scalar curvature equals twice the Chern scalar curvature, revealing special geometric properties.

Contribution

It provides explicit examples of Kähler-like scalar curvature metrics on generalized flag manifolds, advancing understanding of their geometric structures.

Findings

Identification of invariant almost Hermitian structures with $s=2s_{C}$

Construction of examples with Kähler-like scalar curvature

Insights into scalar curvature relations on flag manifolds

Abstract

In this paper we study invariant almost Hermitian geometry on generalized flag manifolds. We will focus on providing examples of K\"ahler like scalar curvature metric, that is, almost Hermitian structures $(g,J)$ satisfying $s=2s_{\rm C}$, where $s$ is Riemannian scalar curvature and $s_{\rm C}$ is the Chern scalar curvature.