Type: Article
Publication Date: 2013-09-30
Citations: 15
DOI: https://doi.org/10.4134/bkms.2013.50.5.1683
In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of <TEX>$f$</TEX> in the warped product space <TEX>$R{\times}_fB$</TEX> with gradient Ricci solitons. Moreover, we construct new examples of non-Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.