Some doubly-warped product gradient Ricci solitons

초록

In this paper, we study certain doubly-warped products which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form g = dx<inf>1</inf> 2+ p(x<inf>1</inf>)2dx2<inf>2</inf> + h(x<inf>1</inf>)2 g ∼ on ℝ2 × N, where x<inf>1</inf>, x<inf>2</inf> are the local coordinates on ℝ2 and g ∼ is an Einstein metric on the manifold N. We obtained a full description of all the possible local gradient Ricci solitons. © 2016 Korean Mathematical Society.

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