About the Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection

Authors

  • Danila S. Grigoryev Altai State University, 61 Lenina Avenue, Barnaul 656049, Russia
  • Dmitrii N. Oskorbin Moscow Institute of Physics and Technology, 9 Institutskij Lane, Dolgoprudnyj 141701, Russia
  • Eugene D. Rodionov Altai State University, 61 Lenina Avenue, Barnaul 656049, Russia

Keywords:

Ricci flow, three-dimensional non-unimodular Lie groups, semisymmetric equiaffine connections

Abstract

The Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection is studied. The Ricci flow equation in the coordinate system proposed by J. Milnor is reduced to systems of algebraic and differential equations. A solution to the Ricci flow equation in the class of left-invariant Milnor metrics is found. The results of works by K. Onda, D. Knopf and K. McLeod concerning the Ricci flow on three-dimensional Lie groups in the case of Levi-Civita connectivity are generalised.

Author Biographies

  • Danila S. Grigoryev, Altai State University, 61 Lenina Avenue, Barnaul 656049, Russia

    masterʼs degree student at the department of mathematical analysis, Institute of Mathematics and Information Technologies

  • Dmitrii N. Oskorbin, Moscow Institute of Physics and Technology, 9 Institutskij Lane, Dolgoprudnyj 141701, Russia

    PhD (physics and mathematics); associate professor at the department of higher mathematics

  • Eugene D. Rodionov, Altai State University, 61 Lenina Avenue, Barnaul 656049, Russia

    doctor of science (physics and mathematics); professor at the department of mathematical analysis, Institute of Mathematics and Information Technologies

References

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  3. Onda K. Ricci flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. arXiv:0906.1035 [Preprint]. 2010 [cited 2010 March 24]: [25 p.]. Available from: https://arxiv.org/abs/0906.1035.
  4. Knopf D, McLeod K. Quasi-convergence of model geometries under the Ricci flow. Communications in Analysis and Geometry. 2001;9(4):879–919. DOI: 10.4310/CAG.2001.v9.n4.a7.
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Published

2025-10-10

Issue

No. 2 (2025): Journal of the Belarusian State University. Mathematics and Informatics

Section

Geometry and Topology

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How to Cite

[1]
Grigoryev, D.S. et al. 2025. About the Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Oct. 2025), 30–41. DOI:https://doi.org/10.33581/2520-6508-2025-2-30-41.