On quaternionic bisectional curvature
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914974916411392 |
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| author | Macia, Oscar Semmelmann, Uwe Weingart, Gregor |
| author_facet | Macia, Oscar Semmelmann, Uwe Weingart, Gregor |
| contents | In this article we study the concept of quaternionic bisectional curvature introduced by B. Chow and D. Yang for quaternion-Kähler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space. We also show that all symmetric quaternion-Kähler manifolds different from the quaternionic projective space admit quaternionic lines of negative quaternionic bisectional curvature. In particular this implies that non-negative sectional curvature does not imply non-negative quaternionic bisectional curvature. Moreover we give a new and rather short proof of a classification result by A. Gray on compact Kähler manifolds of non-negative sectional curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09173 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On quaternionic bisectional curvature Macia, Oscar Semmelmann, Uwe Weingart, Gregor Differential Geometry 53C10, 53C15, 58J50 In this article we study the concept of quaternionic bisectional curvature introduced by B. Chow and D. Yang for quaternion-Kähler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space. We also show that all symmetric quaternion-Kähler manifolds different from the quaternionic projective space admit quaternionic lines of negative quaternionic bisectional curvature. In particular this implies that non-negative sectional curvature does not imply non-negative quaternionic bisectional curvature. Moreover we give a new and rather short proof of a classification result by A. Gray on compact Kähler manifolds of non-negative sectional curvature. |
| title | On quaternionic bisectional curvature |
| topic | Differential Geometry 53C10, 53C15, 58J50 |
| url | https://arxiv.org/abs/2308.09173 |