English Russian
Известия
Izvestiya of Altai State
University Journal
The News of Altai State University

 Архив журнала «Известия АлтГУ», начиная с 2017 г., размещен на новой версии сайта http://izvestiya.asu.ru
 Актуальная информация о журнале размещена на новой версии сайта http://izvestiya.asu.ru

Print ISSN 1561-9443
On-line ISSN 1561-9451
Issues list
Table of Contents
Physical science
Mathematics
About the Journal
Editorial board and Editorial advisory board
Regulations on reviewing research papers
Rules of the articles representation
Publication Ethics of the journal «Izvestiya of Altai State University»
 
1-2(85)2015
  MATHEMATICS

S.V. Pastukhova, O.P. Khromova

On the Signature of Ricci Curvature Tensor Operator of Three-Dimensional Lie Groups with Left-Invariant Lorentzian Metrics

Curvatures of left-invariant Riemannian metrics on Lie groups were studied by J. Milnor. Possible signatures of the Ricci operator were found for the case of three-dimensional Lie groups with leftinvariant Riemannian metric. Further, O. Kowalski and S. Nikcevic found three-dimensional metric Lie groups and three-dimensional Riemannian locally homogeneous spaces with prescribed values of the Ricci operator. Y.G. Nikonorov and A.G. Kremlev identified possible signatures of the Ricci operator on four-dimensional Lie groups with left-invariant Riemannian metric. Similar results for the onedimensional curvature operator and the sectional curvature operator were obtained by D.N. Oskorbin, E.D. Rodionov, O.P. Khromova. In the case of left-invariant Lorentz metrics on Lie groups, the situation is less clear. In this paper, we define the possible signatures of the Ricci tensor operator on three-dimensional Lie group with left-invariant Lorenzian metric. Results of G. Calvaruso, E.D. Rodionov, V.V. Slavskii, L.N. Chibrikova studies on the structure of 3-dimensional homogeneous Lorentzian manifolds are used in our study.

DOI 10.14258/izvasu(2015)1.2-26

Key words: Lie algebras and Lie groups, leftinvariant Lorentzian metrics, Ricci tensor

Full text at PDF, 602Kb. Language: Russian.

PASTUKHOVA S.V.
Altai State University (Barnaul, Russia)
E-mail: pastukhova.svetlana.1992@gmail.com

KHROMOVA O.P.
Altai State University (Barnaul, Russia)
E-mail: khromova.olesya@gmail.com

 

Print Edition of "Izvestiya of Altai State University" © 1996-2017 Altai State University.
All rights reserved. Any of parts of a journal or edition as a whole cannot be reprinted without the written sanction of the authors or publisher. On purchase of a journal to address to ASU publishing house:
Altai State University. 656049, 66 Dimitrova street, Barnaul, Russia. Telephone + 7 (3852) 366351.