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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 6

Some properties of Riemannian geometry of the tangent bundle of Lie groups

Davood SEIFIPOUR
Esmaeil PEYGHAN
Pages
2842–2864
Publication Date
2022-11-05
DOI
—
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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

🎯
Objective & Hypothesis:We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariantRiemannian 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:Domain Parameters

Abstract

We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariantRiemannian 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. (2022). 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/607736

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