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Remarks on Einstein Solitons with Certain Types of Vector Field

Year 2021, , 100 - 105, 15.04.2021
https://doi.org/10.36890/iejg.859572

Abstract

We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and illustrate the result with suitable examples. Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.

References

  • [1] Blaga, A. M.: On warped product gradient η-Ricci solitons. Filomat. 31 (18), 5791-5801 (2017). https://doi.org/10.2298/FIL1718791B
  • [2] Blaga, A. M.: Remarks on almost Riemann solitons with gradient or torse-forming vector field. Preprint arXiv:2008.06413v4 (2020).
  • [3] Blaga, A. M., Özgür, C.: Almost η-Ricci and almost η-Yamabe solitons with torse-forming potential vector field. Quaestiones Math., 1-21 (2020). https://doi.org/10.2989/16073606.2020.1850538
  • [4] Catino, G., Mazzieri, L.: Gradient Einstein solitons. Nonlin. Anal. 132, 66-94 (2016). https://doi.org/10.1016/j.na.2015.10.021
  • [5] Eells, J., Sampson, J. H.: Harmonic Mappings of Riemannian Manifolds. American J. Math. 86 (1), 109-160 (1964). https://doi.org/10.2307/2373037
  • [6] Hamilton, R. S.: The Ricci flow on surfaces. Contemp. Math. 71, 237-262 (1988). https://doi.org/10.1090/conm/071/954419
Year 2021, , 100 - 105, 15.04.2021
https://doi.org/10.36890/iejg.859572

Abstract

References

  • [1] Blaga, A. M.: On warped product gradient η-Ricci solitons. Filomat. 31 (18), 5791-5801 (2017). https://doi.org/10.2298/FIL1718791B
  • [2] Blaga, A. M.: Remarks on almost Riemann solitons with gradient or torse-forming vector field. Preprint arXiv:2008.06413v4 (2020).
  • [3] Blaga, A. M., Özgür, C.: Almost η-Ricci and almost η-Yamabe solitons with torse-forming potential vector field. Quaestiones Math., 1-21 (2020). https://doi.org/10.2989/16073606.2020.1850538
  • [4] Catino, G., Mazzieri, L.: Gradient Einstein solitons. Nonlin. Anal. 132, 66-94 (2016). https://doi.org/10.1016/j.na.2015.10.021
  • [5] Eells, J., Sampson, J. H.: Harmonic Mappings of Riemannian Manifolds. American J. Math. 86 (1), 109-160 (1964). https://doi.org/10.2307/2373037
  • [6] Hamilton, R. S.: The Ricci flow on surfaces. Contemp. Math. 71, 237-262 (1988). https://doi.org/10.1090/conm/071/954419
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Adara-monica Blaga 0000-0003-0237-3866

Dan Radu Laţcu This is me 0000-0003-1201-7400

Publication Date April 15, 2021
Acceptance Date March 30, 2021
Published in Issue Year 2021

Cite

APA Blaga, A.-m., & Laţcu, D. R. (2021). Remarks on Einstein Solitons with Certain Types of Vector Field. International Electronic Journal of Geometry, 14(1), 100-105. https://doi.org/10.36890/iejg.859572
AMA Blaga Am, Laţcu DR. Remarks on Einstein Solitons with Certain Types of Vector Field. Int. Electron. J. Geom. April 2021;14(1):100-105. doi:10.36890/iejg.859572
Chicago Blaga, Adara-monica, and Dan Radu Laţcu. “Remarks on Einstein Solitons With Certain Types of Vector Field”. International Electronic Journal of Geometry 14, no. 1 (April 2021): 100-105. https://doi.org/10.36890/iejg.859572.
EndNote Blaga A-m, Laţcu DR (April 1, 2021) Remarks on Einstein Solitons with Certain Types of Vector Field. International Electronic Journal of Geometry 14 1 100–105.
IEEE A.-m. Blaga and D. R. Laţcu, “Remarks on Einstein Solitons with Certain Types of Vector Field”, Int. Electron. J. Geom., vol. 14, no. 1, pp. 100–105, 2021, doi: 10.36890/iejg.859572.
ISNAD Blaga, Adara-monica - Laţcu, Dan Radu. “Remarks on Einstein Solitons With Certain Types of Vector Field”. International Electronic Journal of Geometry 14/1 (April 2021), 100-105. https://doi.org/10.36890/iejg.859572.
JAMA Blaga A-m, Laţcu DR. Remarks on Einstein Solitons with Certain Types of Vector Field. Int. Electron. J. Geom. 2021;14:100–105.
MLA Blaga, Adara-monica and Dan Radu Laţcu. “Remarks on Einstein Solitons With Certain Types of Vector Field”. International Electronic Journal of Geometry, vol. 14, no. 1, 2021, pp. 100-5, doi:10.36890/iejg.859572.
Vancouver Blaga A-m, Laţcu DR. Remarks on Einstein Solitons with Certain Types of Vector Field. Int. Electron. J. Geom. 2021;14(1):100-5.