Curvature positivity for Kähler and quasi-Kähler flag manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908427152785408 |
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| author | Galindo, Giovane Oliveira, Ailton R. |
| author_facet | Galindo, Giovane Oliveira, Ailton R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature positivity for Kähler and quasi-Kähler flag manifolds Galindo, Giovane Oliveira, Ailton R. Differential Geometry 32Q10, 32Q15, 32Q60, 53C30, 32M10, 14M15 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. |
| title | Curvature positivity for Kähler and quasi-Kähler flag manifolds |
| topic | Differential Geometry 32Q10, 32Q15, 32Q60, 53C30, 32M10, 14M15 |
| url | https://arxiv.org/abs/2506.22672 |