Infinitesimal Transformations of Locally Conformal Kähler Manifolds

Mathematics

Yevhen Cherevko¹  Dana Smetanová²  Volodymyr Berezovski³  Irena Hinterleitner⁴ 

[1] Department of Economic Cybernetics and Information Technologies, Odesa National Economic University, 65082 Odesa, Ukraine;Department of Informatics and Natural Sciences, Faculty of Technology, Institute of Technology and Business in České Budějovice, 37001 Czech Budejovice, Czech Republic;Department of Mathematics and Physics, Uman National University of Horticulture, 20300 Uman, Ukraine;Department of Mathematics, Faculty of Civil Engineering, Brno University of Technology, 60190 Brno, Czech Republic;

关键词: Hermitian manifold;    locally conformal Kähler manifold;    Lee form;    diffeomorphism;    conformal transformation;    Lie derivative;   

DOI  :  10.3390/math7080658

来源: DOAJ

【 摘 要 】

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. We have also obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. We have also calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding Kählerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to some subgroup of the homothetic group of the coresponding local Kählerian metric.

【 授权许可】

Unknown