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.2013.50.5.1683
Published online 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
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