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