Publication detail

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

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

Original Title

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

English Title

Infinitesimal Transformations of Locally Conformal Kähler Manifolds

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

24.07.2019

Publisher

MDPI

ISBN

2227-7390

Periodical

Mathematics

Year of study

8

Number

7

State

CH

Pages from

1

Pages to

16

Pages count

16

URL

Full text in the Digital Library

Documents

BibTex


@article{BUT158228,
  author="Yevhen {Cherevko} and Vladimir {Berezovski} and Irena {Hinterleitner} and Dana {Smetanová}",
  title="Infinitesimal Transformations of Locally Conformal Kähler Manifolds",
  annote="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.",
  address="MDPI",
  chapter="158228",
  doi="10.3390/math7080658",
  howpublished="online",
  institution="MDPI",
  number="7",
  volume="8",
  year="2019",
  month="july",
  pages="1--16",
  publisher="MDPI",
  type="journal article in Web of Science"
}