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Journals / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 1

Classification of some geometric structures on 4-dimensional Riemannian Lie group

Esmaeil PEYGHAN
Davood SEIFIPOUR
Pages
257–276
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 study the space form problem and spectral properties of Szabo operator on G.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study the spectral geometry of a 4-dimensional Lie group.
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Key Findings & Data:The main focus of this paper is to study the 2-Stein and 2-Osserman structures on a 4-dimensional Riemannian Lie group.
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Conclusion & Impact:Finally, we study the space form problem and spectral properties of Szabo operator on G.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we study the spectral geometry of a 4-dimensional Lie group. The main focus of this paper is to study the 2-Stein and 2-Osserman structures on a 4-dimensional Riemannian Lie group. In this paper, we study the spectrum and trace of Jacobi operator and also we study the characteristic polynomial of generalized Jacobi operator on the non-abelian 4-dimensional Lie group G, whenever G is equipped with an orthonormal left invariant Riemannian metric g . The Lie algebra structures in dimension four have key role in this paper. It is known that in the classification of 4-dimensional non-abelian Lie algebras there are nineteen classes of Lie algebras up to isomorphism [12]. We consider these classes and study all of them. Finally, we study the space form problem and spectral properties of Szabo operator on G.

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Cite This Article

PEYGHAN, E., SEIFIPOUR, D. (2022). Classification of some geometric structures on 4-dimensional Riemannian Lie group. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 1, 257–276. https://ajindex.com/articles/607278

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