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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
📌 3 Key Takeaways
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Objective & Hypothesis:We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam.
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Key Findings & Data:We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG.
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Conclusion & Impact:Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cotton tensor · Einstein-like structure · Lie group
Abstract
We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG. Then we study some geometrical tensors on TG such as Cotton, Schouten, Weyl, and Bach tensors, and we also compute projective and concircular and m-projective curvatures on TG. Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
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Cite This Article
SEIFIPOUR, D., PEYGHAN, E. (2019). Some properties of Riemannian geometry of the tangent bundle of Lie groups. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 6, 2842–2864. https://ajindex.com/articles/198159