On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds

  • V. M. Kuzakon’

Abstract

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.
Published
25.03.2015
How to Cite
Kuzakon’V. M. “On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 3, Mar. 2015, pp. 427–430, http://umj.imath.kiev.ua/index.php/umj/article/view/1993.
Section
Short communications