An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold

V. F. Kirichenko; O. E. Arsen'eva; A. R. Rustanov

Geodesic

Parcourir par

An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold

V. F. Kirichenko ; O. E. Arsen'eva ; A. R. Rustanov

Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 519-524

Voir la notice de l'article provenant de la source Math-Net.Ru

Résumé

An example of a concircular vector field on a locally conformally Kähler manifold is constructed and the geometric meaning of its characteristic form is studied. It is proved that the Lie vector of a locally conformally Kähler manifold of constant curvature is a concircular vector field. It is also shown that the class of locally conformally Kähler manifolds of constant curvature is a subclass of the class of locally concircularly nearly Kähler manifolds. Conditions under which a locally conformally Kähler manifold of constant curvature is recurrent are obtained.

Keywords: locally conformally Kähler manifold, concircular vector field, locally concircularly nearly Kähler structure.
Mots-clés : Lie form, conformal transformation of the structure

@article{MZM_2022_111_4_a3,
     author = {V. F. Kirichenko and O. E. Arsen'eva and A. R. Rustanov},
     title = {An {Example} of a {Concircular} {Vector} {Field} on a {Locally} {Conformally} {K\"ahler} {Manifold}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {519--524},
     publisher = {mathdoc},
     volume = {111},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a3/}
}

TY  - JOUR
AU  - V. F. Kirichenko
AU  - O. E. Arsen'eva
AU  - A. R. Rustanov
TI  - An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold
JO  - Matematičeskie zametki
PY  - 2022
SP  - 519
EP  - 524
VL  - 111
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a3/
LA  - ru
ID  - MZM_2022_111_4_a3
ER  -

%0 Journal Article
%A V. F. Kirichenko
%A O. E. Arsen'eva
%A A. R. Rustanov
%T An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold
%J Matematičeskie zametki
%D 2022
%P 519-524
%V 111
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a3/
%G ru
%F MZM_2022_111_4_a3

V. F. Kirichenko; O. E. Arsen'eva; A. R. Rustanov. An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 519-524. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a3/