2017
Том 69
№ 9

All Issues

On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds

Kuzakon’ V. M.


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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 3, pp 487-491.

Citation Example: Kuzakon’ V. M. On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds // Ukr. Mat. Zh. - 2015. - 67, № 3. - pp. 427–430.