Detail publikace

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

CHEREVKO, Y. BEREZOVSKI, V. HINTERLEITNER, I. SMETANOVÁ, D.

Originální název

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

CHEREVKO, Y.; BEREZOVSKI, V.; HINTERLEITNER, I.; SMETANOVÁ, D.

Vydáno

24. 7. 2019

Nakladatel

MDPI

ISSN

2227-7390

Periodikum

Mathematics

Ročník

8

Číslo

7

Stát

Švýcarská konfederace

Strany od

1

Strany do

16

Strany počet

16

URL

https://www.mdpi.com/2227-7390/7/8/658

Plný text v Digitální knihovně

http://hdl.handle.net/11012/184670

BibTex

@article{BUT158228,
  author="Yevhen {Cherevko} and Vladimir {Berezovski} and Irena {Hinterleitner} and Dana {Smetanová}",
  title="Infinitesimal Transformations of Locally Conformal Kähler Manifolds",
  journal="Mathematics",
  year="2019",
  volume="8",
  number="7",
  pages="1--16",
  doi="10.3390/math7080658",
  issn="2227-7390",
  url="https://www.mdpi.com/2227-7390/7/8/658"
}