ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION

Title & Authors
ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION
Kim, Byung Hak; Lee, Sang Deok; Choi, Jin Hyuk; Lee, Young Ok;

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 $\small{f}$ in the warped product space $\small{R{\times}_fB}$ 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.
Keywords
Ricci curvature;Einstein metric;warped product space;
Language
English
Cited by
1.
Gradient Ricci Solitons with Structure of Warped Product, Results in Mathematics, 2017, 71, 3-4, 825
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