Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GRADIENT EINSTEIN-TYPE CONTACT METRIC MANIFOLDS

  • Received : 2019.07.18
  • Accepted : 2020.01.07
  • Published : 2020.04.30
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Abstract

Consider a gradient Einstein-type metric in the setting of K-contact manifolds and (κ, µ)-contact manifolds. First, it is proved that, if a complete K-contact manifold admits a gradient Einstein-type metric, then M is compact, Einstein, Sasakian and isometric to the unit sphere 𝕊2n+1. Next, it is proved that, if a non-Sasakian (κ, µ)-contact manifolds admits a gradient Einstein-type metric, then it is flat in dimension 3, and for higher dimension, M is locally isometric to the product of a Euclidean space 𝔼n+1 and a sphere 𝕊n(4) of constant curvature +4.

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References

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