Remarks on Einstein Solitons with Certain Types of Vector Field

Yıl 2021, Cilt: 14 Sayı: 1, 100 - 105, 15.04.2021

Adara-monica Blaga Dan Radu Laţcu

https://doi.org/10.36890/iejg.859572

Cited By: 1

Öz

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.

Anahtar Kelimeler

Einstein solitons, gradient vector field, concircular vector field

Kaynakça

• [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