In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afi ne 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 $T^*M$.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $M$ be an n-dimensional manifold with a torsion free a fine connection $\nabla$ and let $T^*M$ be the cotangent bundle.
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Key Findings & Data:Let $M$ be an n-dimensional manifold with a torsion free a fine connection $\nabla$ and let $T^*M$ be the cotangent bundle.
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Conclusion & Impact:In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afi ne 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 $T^*M$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:A fine connection · Cyclic parallel · Szabó manifold
Abstract
Let $M$ be an n-dimensional manifold with a torsion free a fine 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 afi ne 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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