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
