대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권1호
  • /
  • Pages.165-171
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  • 2021
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GRADIENT YAMABE SOLITONS WITH CONFORMAL VECTOR FIELD

  • 투고 : 2020.03.27
  • 심사 : 2020.10.19
  • 발행 : 2021.01.31
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초록

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

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참고문헌

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