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Gradient generalized \(\eta \)-Ricci soliton and contact geometry

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Abstract

In this paper, we consider gradient generalized \(\eta \)-Ricci soliton on contact metric manifolds of dimension \(\ge 5\). First, we prove that if a K-contact metric represents a gradient generalized \(\eta \)-Ricci soliton then either it is compact \(\eta \)-Einstein and Sasakian, provided \(\lambda > -2\), or it is compact and isometric to a unit sphere \(S^{2n+1}(1)\). Next we prove that, if a compact contact metric with parallel Ricci tensor represents a non-trivial gradient generalized \(\eta \)-Ricci soliton, then it is locally isometric to \(S^{2n+1}(1)\).

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  1. Department Of Mathematics, Chandernagore College, Hooghly, W.B., 712 136, India

    Amalendu Ghosh

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Ghosh, A. Gradient generalized \(\eta \)-Ricci soliton and contact geometry. J. Geom. 113, 11 (2022). https://doi.org/10.1007/s00022-021-00625-z

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  • DOI: https://doi.org/10.1007/s00022-021-00625-z

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