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

On a classification of warped product spaces with gradient Ricci solitons

Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi

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.

Keywords


Ricci curvature; warped product space; Ricci soliton

Subject classification

53C25, 53B21

Sponsor(s)

Kyung Hee University

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