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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2022.4
- 수록면
- 585 - 594 (10page)
- DOI
- 10.4134/CKMS.c200423
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초록· 키워드
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In this article we classify four dimensional gradient Ricci solitons $(M, g, f)$ with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood $V$ of each point in some open dense subset of $M$, $(V, g)$ is isometric to one of the following: {\rm (i)} an Einstein manifold. {\rm (ii)} a domain in the Riemannian product $ (\mathbb{R}^2, g_0) \times (N, \tilde{g})$, where $g_0$ is the flat metric on $\mathbb{R}^2$ and $(N, \tilde{g})$ is a two dimensional Riemannian manifold of constant curvature $\lambda \neq 0$. {\rm (iii)} a domain in $\mathbb{R} \times W$ with the warped product metric $ ds^2 + h(s)^2 \tilde{g},$ where $\tilde{g}$ is a constant curved metric on a three dimensional manifold $W$.
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