# ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION

• Received : 2012.12.04
• Published : 2013.09.30

#### 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 $R{\times}_fB$ 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.

#### Acknowledgement

Supported by : Kyung Hee University

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#### Cited by

1. Gradient Ricci Solitons with Structure of Warped Product vol.71, pp.3-4, 2017, https://doi.org/10.1007/s00025-016-0583-2