Geodesic
An Example of a Concircular Vector Field on a Locally Conformally K\"ahler Manifold
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 519-524

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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/}
}
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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/