DOI QR코드

DOI QR Code

Ricci-Yamabe Solitons and Gradient Ricci-Yamabe Solitons on Kenmotsu 3-manifolds

  • Received : 2021.02.14
  • Accepted : 2021.06.14
  • Published : 2021.12.31

Abstract

The aim of this paper is to characterize a Kenmotsu 3-manifold whose metric is either a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton. Finally, we verify the obtained results by an example.

Keywords

Acknowledgement

The authors are thankful to the referee for his valuable suggestions towards the improvement of the paper.

References

  1. D. E. Blair, Riemannian Geometry of contact and symplectic manifolds, Progress in Mathematics, 203(2010), Birkhauser, New work.
  2. G. Catino and L. Mazzieri, Gradient Einstein solitons, Nonlinear Anal., 132(2016), 66-94. https://doi.org/10.1016/j.na.2015.10.021
  3. G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza and L. Mazzieri, The Ricci-Bourguignon flow, Pacific J. Math., 28(2017), 337-370. https://doi.org/10.2140/pjm.1969.28.337
  4. U. C. De and G. Pathak, On 3-dimensional Kenmotsu manifolds, Indian J. Pure Appl. Math., 35(2)(2004), 159-165.
  5. D. Dey, Almost Kenmotsu metric as Ricci-Yamabe soliton, arXiv: 2005.02322v1[math.DG] 5 May, 2020.
  6. A. Ghosh, R. Sharma and J. T. Cho, Contact metric manifolds with η-parallel torsion tensor, Ann. Global Anal. Geom., 34(3)(2008), 287-299. https://doi.org/10.1007/s10455-008-9112-1
  7. S. Guler and M. Crasmareanu, Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy, Turkish J. Math., 43(5)(2019), 2631-2641. https://doi.org/10.3906/mat-1902-38
  8. R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., 71(1998), 237-262. https://doi.org/10.1090/conm/071/954419
  9. R. S. Hamilton, Lectures on geometric flows, 1989 (unpublished).
  10. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  11. V. F. Kirichenko, On the geometry of Kenmotsu manifolds, Dokl. Akad. Nauk, 380(5)(2001), 585-587.
  12. S. Sasaki and Y. Hatakeyama, On differentiable manifolds with certain structures which are closely related to almost contact structure, II, Tohoku Math. J., 13(1961), 281-294. https://doi.org/10.2748/tmj/1178244304
  13. Y. Wang, Yamabe soliton on 3-dimensional Kenmotsu manifolds, Bull. Belg. Math. Soc. Simon Stevin, 23(2016), 345-355. https://doi.org/10.36045/bbms/1473186509
  14. K. Yano, Concircular geometry. I. Concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195-200.