Turkish Journal of Mathematics
Abstract
In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
DOI
10.3906/mat-1606-49
Keywords
Ricci curvature, warped product space, Ricci soliton
First Page
1365
Last Page
1375
Recommended Citation
LEE, S. D, KIM, B. H, & CHOI, J. H (2017). Warped product spaces with Ricci conditions. Turkish Journal of Mathematics 41 (6): 1365-1375. https://doi.org/10.3906/mat-1606-49
