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’
Brief Communications

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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  1. 1.
    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
  2. 2.
    A.V. Aminova, Projective Transformations of Pseudo-Riemannian Manifolds [in Russian], Yanus-K, Moscow (2003).Google Scholar
  3. 3.
    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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