Infinitesimal Transformations of Locally Conformal Kähler Manifolds

@article{52501,
   author = {Cherevko, Yevhen and Berezovski, Volodymyr and Hinterleitner, Irena and Smetanová, Dana},
   article_location = {BASEL, SWITZERLAND},
   article_number = {8},
   doi = {http://dx.doi.org/10.3390/math7080658},
   keywords = {Hermitian manifold; locally conformal Kähler manifold; Lee form; diffeomorphism; conformal transformation; Lie derivative},
   language = {eng},
   issn = {2227-7390},
   journal = {Mathematics},
   title = {Infinitesimal Transformations of Locally Conformal Kähler Manifolds},
   url = {https://www.mdpi.com/2227-7390/7/8/658},
   volume = {7},
   year = {2019}
}

TY  - JOUR
ID  - 52501
AU  - Cherevko, Yevhen - Berezovski, Volodymyr - Hinterleitner, Irena - Smetanová, Dana
PY  - 2019
TI  - Infinitesimal Transformations of Locally Conformal Kähler Manifolds
JF  - Mathematics
VL  - 7
IS  - 8
SP  - 1-16
EP  - 1-16
PB  - MDPI
SN  - 22277390
KW  - Hermitian manifold
KW  - locally conformal Kähler manifold
KW  - Lee form
KW  - diffeomorphism
KW  - conformal transformation
KW  - Lie derivative
UR  - https://www.mdpi.com/2227-7390/7/8/658
L2  - https://www.mdpi.com/2227-7390/7/8/658
N2  - 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.
ER  - 

CHEREVKO, Yevhen, Volodymyr BEREZOVSKI, Irena HINTERLEITNER and Dana SMETANOVÁ. Infinitesimal Transformations of Locally Conformal Kähler Manifolds. \textit{Mathematics}. BASEL, SWITZERLAND: MDPI, vol.~7, No~8, p.~1-16. ISSN~2227-7390. doi:10.3390/math7080658. 2019.