Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 109, 30 pages      arXiv:2107.11455      https://doi.org/10.3842/SIGMA.2021.109

Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds

Lino Grama a and Ailton R. Oliveira b
a) IMECC - Universidade Estadual de Campinas (Unicamp), Departamento de Matemática, Rua Sérgio Buarque de Holanda,651, Cidade Universitária Zeferino Vaz. 13083-859 Campinas - SP, Brazil
b) UEMS - Universidade Estadual de Mato Grosso do Sul - MS, Cidade Universitária de Dourados, Rodovia Itahum, Km 12 s/n - Jardim Aeroporto, Dourados - MS, Brazil

Received August 02, 2021, in final form December 11, 2021; Published online December 21, 2021

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 $s=2s_{\rm C}$, where $s$ is Riemannian scalar curvature and $s_{\rm C}$ is the Chern scalar curvature.

Key words: curvature of almost Hermitian structures; generalized flag manifolds; Kähler like scalar curvature.

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