Ukrainian Mathematical Journal

, Volume 67, Issue 3, pp 487–491 | Cite as

On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds

  • V. M. Kuzakon’
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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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References

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    V. F. Kirichenko and V. M. Kuzakon’, “On the geometry of holomorphic developable vector fields on almost Hermitian manifolds,” Ukr. Mat. Zh., 65, No. 7, 1005–1008 (2013); English translation: Ukr. Math. J., 65, No. 7, 1122–1125 (2013).Google Scholar
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    A.V. Aminova, Projective Transformations of Pseudo-Riemannian Manifolds [in Russian], Yanus-K, Moscow (2003).Google Scholar
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    A. Gray and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Math. Pure Appl., 123, 35–58 (1980).MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. M. Kuzakon’
    • 1
  1. 1.Odessa National Academy of Food TechnologiesOdessaUkraine

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