Some characterizations of hyperbolic Ricci solitons on nearly cosymplectic manifolds with respect to the Tanaka-Webster connection

Abstract

It is known that a hyperbolic Ricci soliton is one of the generalization of the Ricci solitons and it is a Riemannian manifold (𝑀, 𝑔) furnished with a differentiable vector field 𝑈 on 𝑀 and two real numbers 𝜆 and 𝜇 ensuring 𝑅𝑖𝑐 + 𝜆𝐿𝑈𝑔 + 1 2 𝐿𝑈 (𝐿𝑈𝑔) = 𝜇𝑔, where 𝐿𝑈 denotes the Lie derivative with respect to the vector field 𝑋 on 𝑀. Furthermore, hyperbolic Ricci solitons yield similar solutions to hyperbolic Ricci flow. In this paper, we study hyperbolic Ricci solitons on nearly cosymplectic manifolds endowed with the Tanaka-Webster connection. We give some results for these manifolds when the potential vector field is a pointwise collinear with the Reeb vector field and a concircular vector field.

Keywords

• hyperbolic Ricci soliton
• nearly cosymplectic manifold
• Tanaka
• Webster connection

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