Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(5): 1683-1691

Printed September 1, 2013

https://doi.org/10.4134/BKMS.2013.50.5.1683

Copyright © The Korean Mathematical Society.

On warped product spaces with a certain Ricci condition

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