Abstract
In this paper, we introduce the new concept of gradient h-almost η-Ricci soliton. We discuss here a steady or expanding gradient h-almost η-Ricci soliton warped product Bn ×f Fm, m 1. We show that the warping function f of this warped product attains minimum as well as maximum and it will definitely be a Riemannian product under certain conditions. We also describe some suitable restrictions to these constructions for the compact base of this warped product. Later, we study h-almost η-Ricci soliton and gradient h-almost η-Ricci soliton on warped product manifolds including a concurrent vector field.
Publisher
Sociedade Paranaense de Matemática
Reference20 articles.
1. A. L. Besse, Einstein manifolds, Ergebnisse Der Mathematik und ihrer Grenzgebiete. 3. [Results in Mathematics and Related Areas (3)], Vol. 10, Springer-Verlag, Berlin , 1987.
2. A. Barros, R. Batista, E. Ribeiro Jr., Bounds on volume growth of geodesic balls for Einstein warped products, Proc. Amer. Math. Soc. 143, pp. 4415-4422, 2015
3. R. L. Bishop, B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145, pp. 1-49, 1969.
4. Blaga A. M, Tastan H. M., Gradient solitons on doubly warped product manifolds. Reports on Mathematical Physics 89, 319-333, (2022).
5. H. W. Brinkmann, Einstein spaces which are mapped conformally on each other, Math. Ann. 94, pp. 119-145, 1925.