Basu, Nirabhra; Bhattacharyya, Arindam; Dutta, Tamalika Almost conformal Ricci soliton and \(\eta\)-Ricci soliton on 3-dimensional \((\epsilon, \delta)\) trans-Sasakian manifold. (English) Zbl 1399.53123 Bull. Transilv. Univ. Brașov, Ser. III, Math. Inform. Phys. 10(59), No. 2, 13-30 (2017). Summary: In this paper we have shown that if a 3-dimensional \((\epsilon, \delta)\) trans-Sasakian manifold admits conformal Ricci soliton \((g, V, \lambda)\) and the vector field \(V\) is point wise collinear with the unit vector field \(\xi\) then \(V\) is a constant multiple of \(\xi\). Similarly, we have proved that under the same condition an almost conformal Ricci soliton becomes conformal Ricci soliton. We have also studied \(\eta\)-Ricci soliton on \((\epsilon, \delta)\) trans-Sasakian manifold. Finally, we have shown that if a 3-dimensional \((\epsilon, \delta)\) trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton then the manifold is an Einstein manifold. MSC: 53D10 Contact manifolds (general theory) 53D15 Almost contact and almost symplectic manifolds 53A30 Conformal differential geometry (MSC2010) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:trans-Sasakian manifold; conformal Ricci soliton; almost conformal Ricci soliton; \(\eta\)-Ricci soliton; conformal gradient shrinking Ricci soliton PDFBibTeX XMLCite \textit{N. Basu} et al., Bull. Transilv. Univ. Brașov, Ser. III, Math. Inform. Phys. 10(59), No. 2, 13--30 (2017; Zbl 1399.53123)