η-Ricci solitons on contact pseudo-metric manifolds

2021/03/08 by Asgharzadeh, Eftekhar, Faghfouri, Morteza
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.05052

Abstract

In this paper, we prove that a Sasakian pseudo-metric manifold which admits an η-Ricci soliton is an η-Einstein manifold, and if the potential vector field of the η-Ricci soliton is not a Killing vector field then the manifold is D-homothetically fixed, and the vector field leaves the structure tensor field invariant. Next, we prove that a K-contact pseudo-metric manifold with a gradient η-Ricci soliton metric is η-Einstein. Moreover, we study contact pseudo-metric manifolds admitting an η-Ricci soliton with a potential vector field point-wise colinear with the Reeb vector field. Finally, we study gradient η-Ricci solitons on (κ, μ)-contact pseudo-metric manifolds.

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