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K-contact and (k, μ)-contact metric as a generalized η-Ricci soliton

  • Amalendu Ghosh
Published/Copyright: February 15, 2023
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Abstract

Using generalized Pohozaev-Schoen integral identity, we prove that a compact K-contact manifold of dimension >3 admitting a proper η-Ricci almost soliton is isometric to a unit sphere S2n+1 provided its scalar curvature is constant. Next, it is proved that if a (k, μ)-contact metric represents a non-trivial gradient generalized η-Ricci soliton, then M is flat in dimension 3 and in higher dimensions M is either η-Einstein or locally isometric to En+1  ×  Sn(4).

  1. (Communicated by Július Korbaš)

Acknowledgement

The author is very much thankful to the reviewer for some valuable comments towards the improvement of the paper.

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Received: 2021-04-23
Accepted: 2022-01-28
Published Online: 2023-02-15
Published in Print: 2023-02-23

© 2023 Mathematical Institute Slovak Academy of Sciences

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