2018
Том 70
№ 11

All Issues

Kuzakon’ V. M.

Articles: 2
Brief Communications (Russian)

On the Holomorphy of Developable Vector Fields on Almost Hermitian Manifolds

Kuzakon’ V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 3. - pp. 427–430

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.

Brief Communications (Russian)

On the Geometry of Holomorphic Developable Vector Fields on Almost Hermitian Manifolds

Kirichenko V. F., Kuzakon’ V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 1005–1008

The determination of conditions for the invariance of geometric objects under the action of a group of transformations is one of the most important problems of geometric research. We study the invariance conditions for almost Hermitian structures relative to the action of a local one-parameter group of diffeomorphisms generated by a developable vector field on a manifold. Moreover, we investigate the relationship between developable (in particular, concircular) vector fields on Riemannian manifolds and locally concircular transformations of the metric of these manifolds.