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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.
📌 3 Key Takeaways
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Objective & Hypothesis:We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field.
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Key Findings & Data:We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and illustrate the result with suitable examples.
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Conclusion & Impact:Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Einstein solitons · gradient vector field · concircular vector field
Abstract
We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and illustrate the result with suitable examples. Moreover, we deduce some geometric properties when the Ricci curvature tensor of the manifold satisfies certain symmetry conditions.
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Cite This Article
BLAGA, A., LA¸TCU, D. R. (2022). Remarks on Einstein Solitons with Certain Types of Vector Field. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 100–105. https://ajindex.com/articles/539581