Korean J. Math. Vol. 24 No. 4 (2016) pp.627-636
DOI: https://doi.org/10.11568/kjm.2016.24.4.627

On a classification of warped product spaces with gradient Ricci solitons

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Published: Dec 30, 2016
Keywords:
Ricci curvature, warped product space, Ricci soliton
Mathematics Subject Classification:
53C25, 53B21

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Sang Deok Lee
Department of Mathematics Dankook University Cheonan 31116, Republic of Korea
Byung Hak Kim
Department of Applied Mathematics Kyung Hee University Yongin 17104, Republic of Korea
Jin Hyuk Choi
Humanitas college Kyung Hee University Yongin 17104, Republic of Korea

Abstract

In this paper, we study Ricci solitons, gradient Ricci solitons in the warped product spaces and gradient Yamabe solitons in the Riemannian product spaces. We obtain the necessary and sufficient conditions for the Riemannian product spaces to be Ricci solitons. Moreover we classify the warped product space which admit gradient Ricci solitons under some conditions of the potential function.


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Kyung Hee University

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