On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds
We introduce the notion of absolutely developable and biholomorphic vector fields defined on almost Hermitian manifolds. It is shown that any developable vector field on a K¨ahlerian manifold is an absolutely developable vector field. It is also proved that, on a nearly Kählerian manifold, an absolu...
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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2015
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1993 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We introduce the notion of absolutely developable and biholomorphic vector fields defined on almost Hermitian manifolds. It is shown that any developable vector field on a K¨ahlerian manifold is an absolutely developable vector field. It is also proved that, on a nearly Kählerian manifold, an absolutely developable vector field ξ preserves the almost complex structure if and only if ξ is a special concircular vector field. In addition, we conclude that, on a quasi-Kählerian or Hermitian manifold, a biholomorphic vector field ξ is a special concircular vector field. |
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