대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권3호
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  • Pages.825-837
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  • 2022
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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STUDY OF GRADIENT SOLITONS IN THREE DIMENSIONAL RIEMANNIAN MANIFOLDS

  • 투고 : 2021.02.06
  • 심사 : 2022.01.19
  • 발행 : 2022.07.31
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초록

We characterize a three-dimensional Riemannian manifold endowed with a type of semi-symmetric metric P-connection. At first, it is proven that if the metric of such a manifold is a gradient m-quasi-Einstein metric, then either the gradient of the potential function 𝜓 is collinear with the vector field P or, λ = -(m + 2) and the manifold is of constant sectional curvature -1, provided P𝜓 ≠ m. Next, it is shown that if the metric of the manifold under consideration is a gradient 𝜌-Einstein soliton, then the gradient of the potential function is collinear with the vector field P. Also, we prove that if the metric of a 3-dimensional manifold with semi-symmetric metric P-connection is a gradient 𝜔-Ricci soliton, then the manifold is of constant sectional curvature -1 and λ + 𝜇 = -2. Finally, we consider an example to verify our results.

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과제정보

We would like to thank the referee and editor for reviewing the paper carefully and their valuable comments to improve the quality of the paper.

참고문헌

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