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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 4

On twisted Riemannian extensions associated with Szabó metrics

Fortuné MASSAMBA
Abdoul Salam DİALLO
Silas LONGWAP
Pages
593–601
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let $M$ be an n-dimensional manifold with a torsion free afine connection $\nabla$ and let $T^*M$ be the cotangent bundle.
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Key Findings & Data:In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afine geometry of $(M,\nabla)$ and the neutral signature pseudo-Riemannian geometry of $T^*M$.
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Conclusion & Impact:We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Afine connection · Cyclic parallel · Szabó manifold

Abstract

Let $M$ be an n-dimensional manifold with a torsion free afine connection $\nabla$ and let $T^*M$ be the cotangent bundle. In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afine geometry of $(M,\nabla)$ and the neutral signature pseudo-Riemannian geometry of $T^*M$. We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.

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Cite This Article

MASSAMBA, F., DİALLO, A. S., LONGWAP, S. (2022). On twisted Riemannian extensions associated with Szabó metrics. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 4, 593–601. https://ajindex.com/articles/529914

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