대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제49권3호
  • /
  • Pages.655-667
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  • 2012
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

  • 투고 : 2011.03.16
  • 발행 : 2012.05.31
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초록

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

키워드

참고문헌

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피인용 문헌

  1. A note on critical point metrics of the total scalar curvature functional vol.424, pp.2, 2015, https://doi.org/10.1016/j.jmaa.2014.11.040
  2. THREE DIMENSIONAL CRITICAL POINT OF THE TOTAL SCALAR CURVATURE vol.50, pp.3, 2013, https://doi.org/10.4134/BKMS.2013.50.3.867
  3. Critical metrics of the total scalar curvature functional on 4-manifolds vol.288, pp.16, 2015, https://doi.org/10.1002/mana.201400390
  4. Brown–York mass and positive scalar curvature II: Besse’s conjecture and related problems pp.1572-9060, 2019, https://doi.org/10.1007/s10455-019-09653-0