The algebraic Ricci solitons of Lie groups H2 × R and Sol3

Document Type : Original Article

Authors

1 Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab 5551395133, Iran. E-mail: p.atashpeykar@ubonab.ac.ir

2 Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab 5551395133, Iran. E-mail: haji.badali@ubonab.ac.ir

Abstract

In this article, we study the algebraic Ricci solitons of three-dimensional Lie group H2×R, endowed with a left-invariant Riemannian metric. Also, we examine the existence of sol-solitons on the three-dimensional Lie group Sol3, endowed with a left-invariant Riemannian metric.

Keywords

References

  • 1. W. Batat, K. Onda, Algebraic Ricci solitons on three-dimensional Lorentzian Lie groups,
    Springer, New York, (2012).
  • 2. L. Belarbi, Ricci solitons of the H2 × R Lie group, electronic research archive, 28 (2020),
    157–163.
  • 3. L. Belarbi, Ricci solitons of the Sol3 Lie group, Authorea, (2020).
  • 4. A. Fialkow, Hypersurfaces of a space of constant curvature, Ann. of Math. 39 (1938),
    762–785 .
  • 5. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential. Geom,
    17(2) (1982), 255-306.
  • 6. R. S. Hamilton, The Ricci flow on surfaces, J. Differ. Geom. 17 (1982), 255-306.
  • 7. M. Jablonski, Homogeneous Ricci solitons, J. Reine Angew. Math., 699 (2015), 159-182.
  • 8. M. Jablonski, Homogeneous Ricci solitons are algebraic, Geom. Topol., 18 (2014), 2477-
    2486.
  • 9. J. Lauret, Ricci soliton homogeneous nilmanifolds, Math. Ann. 319(4) (2001), 715–733.
  • 10. K. Onda, Examples of algebraic Ricci solitons in the pseudo-Riemannian case, Springer,
    New York, (2014).
  • 11. G. Perelman, The entropy formula for the Ricci flow and its geometric applications,
    (arXiv: 0211159) (2002).
  • 12. H. R. Salimi Moghaddam, Left-invariant Ricci solitons on three-dimensional Lie groups,
    J. Lie Theory 29 (2019), No. 4, 957-968. 
Journal of Finsler Geometry and its Applications
Volume 1, Issue 2
December 2020
Pages 105-114

Files

Share

How to cite

Statistics