대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권2호
  • /
  • Pages.631-634
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  • 2022
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON STATIC MANIFOLDS AND ALMOST RICCI SOLITONS

  • 투고 : 2021.05.12
  • 심사 : 2021.09.23
  • 발행 : 2022.04.30
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⟨ 이전 논문 다음 논문 ⟩

초록

In this short paper, we investigate the existence of non-trivial almost Ricci solitones on static manifolds. As a result we show any compact nontrivial static manifold is isometric to a Euclidean sphere.

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참고문헌

  1. A. Barros, R. Batista, and E. Ribeiro, Jr., Compact almost Ricci solitons with constant scalar curvature are gradient, Monatsh. Math. 174 (2014), no. 1, 29-39. https://doi.org/10.1007/s00605-013-0581-3
  2. J. Corvino, Scalar curvature deformation and a gluing construction for the Einstein constraint equations, Comm. Math. Phys. 214 (2000), no. 1, 137-189. https://doi.org/10.1007/PL00005533
  3. J. Li and C. Xia, An integral formula for affine connections, J. Geom. Anal. 27 (2017), no. 3, 2539-2556. https://doi.org/10.1007/s12220-017-9771-x
  4. S. Pigola, M. Rigoli, M. Rimoldi, and A. G. Setti, Ricci almost solitons, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 10 (2011), no. 4, 757-799.
  5. J. Qing and W. Yuan, On scalar curvature rigidity of vacuum static spaces, Math. Ann. 365 (2016), no. 3-4, 1257-1277. https://doi.org/10.1007/s00208-015-1302-0
  6. X. Wang and Y.-K. Wang, Brendle's inequality on static manifolds, J. Geom. Anal. 28 (2018), no. 1, 152-169. https://doi.org/10.1007/s12220-017-9814-3