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.
๐ 3 Key Takeaways
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Objective & Hypothesis:It is known that a hyperbolic Ricci soliton is one of the generalization of the Ricci solitons and it is a Riemannian manifold (๐, ๐) furnished with a differentiable vector field ๐ on ๐ and two real numbers ๐ and ๐ ensuring ๐ ๐๐ + ๐๐ฟ๐๐ + 1 2 ๐ฟ๐ (๐ฟ๐๐) = ๐๐, where ๐ฟ๐ denotes the Lie derivative with respect to the vector field ๐ on ๐.
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Key Findings & Data:Furthermore, hyperbolic Ricci solitons yield similar solutions to hyperbolic Ricci flow.
๐ก
Conclusion & Impact: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.
It is known that a hyperbolic Ricci soliton is one of the generalization of the Ricci solitons and it is a Riemannian manifold (๐, ๐) furnished with a differentiable vector field ๐ on ๐ and two real numbers ๐ and ๐ ensuring ๐ ๐๐ + ๐๐ฟ๐๐ + 1 2 ๐ฟ๐ (๐ฟ๐๐) = ๐๐, where ๐ฟ๐ denotes the Lie derivative with respect to the vector field ๐ on ๐. 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.
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