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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| Datum: | 2015 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2015
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1993 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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