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 On warped product spaces with a certain Ricci condition Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1683-1691 https://doi.org/10.4134/BKMS.2013.50.5.1683Printed September 1, 2013 Byung Hak Kim, Sang Deok Lee, Jin Hyuk Choi, and Young Ok Lee Kyung Hee University, Dankook University, Kyung Hee University, Kyung Hee University Abstract : 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 $f$ in the warped product space $R \times _f B$ 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. Keywords : Ricci curvature, Einstein metric, warped product space MSC numbers : Primary 53C25, 53B21 Downloads: Full-text PDF