대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권2호
  • /
  • Pages.585-594
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  • 2022
  • /
  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GRADIENT RICCI SOLITONS WITH HALF HARMONIC WEYL CURVATURE AND TWO RICCI EIGENVALUES

  • Kang, Yutae (Department of Mathematics Sogang University) ;
  • Kim, Jongsu (Department of Mathematics Sogang University)
  • 투고 : 2020.11.08
  • 심사 : 2020.11.23
  • 발행 : 2022.04.30
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초록

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: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ2, g0) × (N, ${\tilde{g}}$), where g0 is the flat metric on ℝ2 and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × 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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과제정보

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1A2B5B01001862).

참고문헌

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