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SOME DOUBLY-WARPED PRODUCT GRADIENT RICCI SOLITONS

Kim, Jongsu

  • Received : 2015.08.02
  • Published : 2016.07.31

Abstract

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 $g=dx^2_1+p(x_1)^2dx^2_2+h(x_1)^2\;{\tilde{g}}$ 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 local gradient Ricci solitons.

Keywords

gradient Ricci soliton;harmonic Weyl tensor

References

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)