Paracontact Metric Structures on Five-dimensional Unsolvable Lie Algebras

УДК 514.76

  • Anastasia A. Volkova Kemerovo State University, Kemerovo, Russia Email: aaav9414@gmail.com
  • Nikolay K. Smolentsev Kemerovo State University, Kemerovo, Russia Email: smolennk@mail.ru
DOI_disc_logo https://doi.org/10.14258/izvasu(2024)1-13
Keywords: five-dimensional contact Lie algebras, para-contact metric structures, unsolvable contact Lie algebras

Abstract

This paper studies the problem of the existence of para-contact metric structures and parasasakian structures on five-dimensional unsolvable Lie algebras. According to the classification by A. Diatta, there are three such Lie algebras. These are the decomposable aff(K)xsl(2,K), aff(K)xso(3) ) Lie algebras and the indecomposable sl(2,K)xp К2 Lie algebra, where p is the usual action of sl(2,K) on К2. Decomposable Lie algebras are direct products of the exact symplectic aff(K) Lie algebra and three-dimensional contact Lie algebras.

For an indecomposable sl(2,K)xp К2 Lie algebra, Diatta gives a procedure for constructing a contact struc-ture. Each Lie algebra is considered in detail. It is shown that para-sasakian structures exist only on aff(K)xsl(2,K). Their explicit expressions, Ricci tensors, and scalar cur-vatures are obtained. It is shown that there are paracontact metric structures for other aff(K)xso(3) and sl(2,K)xp К2 Lie algebras, but none of them have the K-paracontact property. Examples of paracontact metric structures are provided for the last two Lie algebras indicated above.

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Author Biographies

Anastasia A. Volkova, Kemerovo State University, Kemerovo, Russia

Undergraduate Student of the Institute of Basic Sciences

Nikolay K. Smolentsev, Kemerovo State University, Kemerovo, Russia

Doctor of Sciences in Physics and Mathematics, Professor of the Department of Fundamental Mathematics

References

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Published
2024-04-05
How to Cite
Volkova A. A., Smolentsev N. K. Paracontact Metric Structures on Five-dimensional Unsolvable Lie Algebras // Izvestiya of Altai State University, 2024, № 1(135). P. 95-100 DOI: 10.14258/izvasu(2024)1-13. URL: http://izvestiya.asu.ru/article/view/%282024%291-13.
Issue
No 1(135) (2024): Известия Алтайского государственного университета
Section
Математика и механика

Copyright (c) 2024 Анастасия Александровна Волкова, Николай Константинович Смоленцев

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