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Ailton R. Oliveira

Publications and source records attributed to Ailton R. Oliveira.

5 recordsLinked to original sources
arXiv2026

Invariant almost Hermitian structures on the maximal real flag manifold of type $\mathcal{A}_3$

We study the Gray-Hervella classes of invariant almost Hermitian structures on the maximal real flag manifold of type $\mathcal{A}_3$. We first obtain an explicit parametrization of all invariant almost Hermitian structures and establish necessary and sufficient conditions for an invariant almost Hermitian structure to belong to each Gray-Hervella class. For each nonempty class, we give an explicit parametrization of the corresponding set of structures, describe it as a smooth manifold and determine its dimension.

math.DG↗
arXiv2025

Curvature positivity for Kähler and quasi-Kähler flag manifolds

In this paper, we study the notions of Griffiths and dual-Nakano positivity for the curvature of the Chern connection on Kähler and quasi-Kähler flag manifolds, as well as for the complex projective space. In this setting, we prove that every flag manifold endowed with a complex structure admits a metric of dual-Nakano semi-positive curvature, and we give a full classification of Kähler flag manifolds with Griffiths semi-positive curvature. Next we prove a series of restrictions for a quasi-Kähler flag manifold to have Griffiths semi-positive curvature, and we conjecture that in fact, there are no such metrics for non-integrable almost-complex structures. Lastly, we give a full classification on invariant metrics on the complex projective space with Griffiths and dual-Nakano semi-positive curvature.

math.DG↗
arXiv2022

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

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.

math.DG↗