Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2016; 31(3): 625-635

Printed July 31, 2016

https://doi.org/10.4134/CKMS.c150141

Copyright © The Korean Mathematical Society.

Some doubly-warped product gradient Ricci solitons

Jongsu Kim

Sogang University

Abstract

In this paper, we study certain doubly-warped products \linebreak which admit gradient Ricci solitons with harmonic Weyl curvature and non-constant soliton function. The metric is of the form $g=dx_1^2 + p(x_1)^2 dx_2^2 + h( x_1 )^2 \ \tilde{g}$ on $\mathbb{R}^2 \times N$, where $x_1, x_2$ are the local coordinates on $\mathbb{R}^2$ and $\tilde{g}$ is an Einstein metric on the manifold $N$. We obtained a full description of all the possible {\it local} gradient Ricci solitons.

Keywords: gradient Ricci soliton, harmonic Weyl tensor

MSC numbers: Primary 53C21, 53C25

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