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 
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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/

[1] A. V. Aminova, Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii, Yanus-K, M., 2003

[2] V. F. Kirichenko, Differentsialno-geometricheskie struktury na mnogoobraziyakh, Pechatnyi Dom, Odessa., 2013

[3] V. F. Kirichenko, “Konformno-ploskie lokalno konformno-kelerovy mnogoobraziya”, Matem. zametki, 51:5 (1992), 57–66 | MR | Zbl

[4] P. Liberman, “Sur les structures presque complexes et autres structures infinitesimales regulieres”, Bull. Soc. Math. France, 83 (1955), 195–224 | DOI | MR | Zbl

[5] I. Vaisman, “On locally and globally conformal Kahler manifolds”, Trans. Amer. Math. Soc., 1262 (1980), 533–541 | MR

[6] A. Gray, L. Vanhecke, “Almost Hermitian manifolds with constant holomorphic sectional curvature”, Časopis Pěst. Mat., 104 (1979), 170–179 | MR | Zbl

[7] V. F. Kirichenko, L. I. Vlasova, “Kontsirkulyarnaya geometriya priblizhenno kelerovykh mnogoobrazii”, Matem. sb., 193:5 (2002), 53–76 | DOI | MR | Zbl