On Connections and their Curvatures
Gustavo Amilcar Salda\~na Moncada, Gregor Weingart
TL;DR
This paper explores the mathematical properties of connections on various types of fiber bundles and examines how these connections relate to their curvatures, providing insights into their geometric structure.
Contribution
It offers a concise analysis of connections on fiber, principal, and vector bundles and investigates their relationships with curvature, enhancing understanding of bundle geometry.
Findings
Connections on different bundles are characterized and compared.
Relations between connections and their curvatures are elucidated.
Foundational insights into bundle geometry are provided.
Abstract
This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Advanced Numerical Analysis Techniques