[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.5.1683

ON WARPED PRODUCT SPACES WITH A CERTAIN RICCI CONDITION

Kim, Byung Hak (Department of Applied Mathematics Kyung Hee University)
Lee, Sang Deok (Department of Applied Mathematics Dankook University)
Choi, Jin Hyuk (Humanitas College Kyung Hee University)
Lee, Young Ok (Department of Mathematics Kyung Hee University)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1683-1691 More about this Journal

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.

Keywords

Ricci curvature; Einstein metric; warped product space;

Citations & Related Records

Reference

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