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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.
📌 3 Key Takeaways
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Objective & Hypothesis:In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles.
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Key Findings & Data:In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles.
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Conclusion & Impact:Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Principal bundle · Assosiated bundle · Induced connection
Abstract
In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles. Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.
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Cite This Article
Abbassi, M. T. K., Lakrini, I. (2022). A note on induced connections. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1737–1744. https://ajindex.com/articles/529510