Some doubly-warped product gradient Ricci solitons
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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.
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.
참고문헌 (6)
- Chow, "The Ricci flow: Techniques and applications, Part I" (2007), American Mathematical Society
- M. Fernandez-Lopez, "Rigidity of shrinking Ricci solitons", Math. Z, 269(1-2), pp.461~466 (2011)
- T. Ivey, "New examples of complete Ricci solitons", Proc. Amer. Math. Soc, 122(1), pp.241~245 (1994)
- T. Ivey, "Local existence of Ricci solitons", Manuscripta Math, 91(2), pp.151~162 (1996)
- J. Kim, "On a classification of four dimensional gradient Ricci solitons with harmonic Weyl curvature", J. Geom. Anal
- O. Munteanu, "On gradient Ricci solitons", J. Geom. Anal, 23(2), pp.539~561 (2013)