principal bundle
[ˈprɪnsəpəl ˈbʌndəl]
nounpl: principal bundles
fibrado principal
1. In differential geometry and topology, a fiber bundle where the fibers are principal homogeneous spaces of a Lie group G, and the structure group acts on itself by left multiplication
The principal bundle P(M, G) is constructed over the manifold M with structure group G.
O fibrado principal P(M, G) é construído sobre a variedade M com grupo de estrutura G.
2. A mathematical object that generalizes the notion of a vector bundle by allowing fibers that are group spaces rather than vector spaces
Connections on principal bundles provide a framework for parallel transport on manifolds.
Conexões em fibrados principais fornecem um marco para transporte paralelo em variedades.
This is a specialized term used exclusively in higher mathematics, differential geometry, and theoretical physics. It is part of the formal academic vocabulary in both Brazilian and European Portuguese-speaking universities. The term has no cultural or regional variations beyond the technical discipline itself. It appears commonly in graduate-level mathematics courses and research papers on topology and gauge theory.
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