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Invariant Ricci Solitons on Three-Dimensional Metric Lie Groups with Semi-Symmetric Connection

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Abstract

In this paper, we investigate invariant Ricci solitons, an important subclass in the class of homogeneous Ricci solitons. A classification of invariant Ricci solitons on three-dimensional Lie groups with left-invariant Riemannian metric and semi-symmetric connection different from the Levi-Civita connection is obtained. It is proved that in this case there exist invariant Ricci solitons with non-conformally Killing vector field.

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Authors and Affiliations

  1. Altai State University, 61 Lenina Ave., 656049, Barnaul, Russia

    P. N. Klepikov

  2. Altai State University, 61 Lenina Ave., 656049, Barnaul, Russia

    E. D. Rodionov & O. P. Khromova

Authors
  1. P. N. Klepikov
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  2. E. D. Rodionov
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  3. O. P. Khromova
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Corresponding authors

Correspondence to P. N. Klepikov, E. D. Rodionov or O. P. Khromova.

Additional information

Communicated by S. K. Vodopianov.

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 8, pp. 80–85.

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Klepikov, P.N., Rodionov, E.D. & Khromova, O.P. Invariant Ricci Solitons on Three-Dimensional Metric Lie Groups with Semi-Symmetric Connection. Russ Math. 65, 70–74 (2021). https://doi.org/10.3103/S1066369X21080090

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  • DOI: https://doi.org/10.3103/S1066369X21080090

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