대한수학회지 (Journal of the Korean Mathematical Society)

  • 제57권2호
  • /
  • Pages.539-552
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  • 2020
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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GRADIENT ALMOST RICCI SOLITONS WITH VANISHING CONDITIONS ON WEYL TENSOR AND BACH TENSOR

  • Co, Jinseok (Department of Mathematics Chung-Ang University) ;
  • Hwang, Seungsu (Department of Mathematics Chung-Ang University)
  • 투고 : 2019.03.08
  • 심사 : 2019.04.24
  • 발행 : 2020.03.01
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초록

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

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참고문헌

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