Curvature positivity for K\"ahler and quasi-K\"ahler flag manifolds

Giovane Galindo; Ailton R. Oliveira

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arXiv · 2506.22672

Curvature positivity for K\"ahler and quasi-K\"ahler flag manifolds

Giovane Galindo·Ailton R. Oliveira

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Abstract

In this paper, we study the notions of Griffiths and dual-Nakano positivity for the curvature of the Chern connection on K\"ahler and quasi-K\"ahler 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 K\"ahler flag manifolds with Griffiths semi-positive curvature. Next we prove a series of restrictions for a quasi-K\"ahler 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.

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BibTeX RIS

Giovane Galindo, Ailton R. Oliveira. 2025-06-27. Curvature positivity for K\"ahler and quasi-K\"ahler flag manifolds. https://arxiv.org/abs/2506.22672

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