Remarks on Einstein Solitons with Certain Types of Vector Field
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.
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- [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
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2008
- Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu