Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME RESULTS IN η-RICCI SOLITON AND GRADIENT ρ-EINSTEIN SOLITON IN A COMPLETE RIEMANNIAN MANIFOLD

  • Received : 2018.08.14
  • Accepted : 2019.02.27
  • Published : 2019.10.31
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Abstract

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient ${\rho}$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient ${\rho}$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost ${\eta}$-Ricci soliton.

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References

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