Results 261 to 270 of about 2,362,828 (289)

Principal bundles

2011
exaly   +2 more sources

Principal Bundles

2020
This chapter examines principal bundles. Throughout the chapter, G will be a topological group. It then defines a principal G-bundle and provides a criterion for a map to be a principal G-bundle. This is followed by several examples of principal G-bundles.
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Cohomology of Flat Principal Bundles

Proceedings of the Edinburgh Mathematical Society, 2018
AbstractWe invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie groupGis naturally isomorphic to the de Rham cohomologyH*dR(G) itself. Then, we show that when a flat connectionAexists on a principalG-bundleP, we may construct a homomorphismEA:H*dR(G)→H*dR(P), which eventually shows that the bundle satisfies a ...
Byun, Yanghyun, Kim, Joohee
openaire   +1 more source

Recent results on vector bundles, principal bundles and related topics

Indian Journal of Pure and Applied Mathematics, 2019
This is a short survey of the interesting work in the theory of vector bundles (with various augmenting structures), principal bundles and related topics by Indian mathematicians in the last decade.
Usha Bhosle
exaly   +2 more sources

A covering property in principal bundles

2018
Summary: Let \(p:X\to B\) be a locally trivial principal \(G\)-bundle and \(\widetilde{p}:\widetilde{X}\to B\) be a locally trivial principal \(\widetilde{G}\)-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that \(\widetilde{G}\) is a covering group of \(G\) if and only if \(\widetilde{X}\)
Pakdaman, A., Attary, M.
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Stable Pairs and Principal Bundles

The Quarterly Journal of Mathematics, 2000
Let \(K\) be a connected compact Lie group, \(G\) its complexification, \(X\) a compact Kähler manifold, and \(E\to X\) be a principal holomorphic \(G\)-bundle over \(X\). Let \(W\) be a complex vector space and \(\rho: K\to U(W)\) a unitary representation of \(K\), which lifts to a representation \(\widetilde\rho\) of \(G\) and let \(V\to X\) be the ...
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Connections on principal prolongations of principal bundles

Differential Geometry and Its Applications, 2008
We study the principal connections on the r-th principal prolongation of a principal bundle by using the related Lie algebroids. We deduce that both approaches to the concept of torsion are naturally equivalent. Special attention is paid to the flow prolongation of connections.
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Vector bundles and principal bundles

2021
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Connections on Principal Bundles

2015
The topic of this chapter has become standard in modern treatments of differential geometry. The very words of the title have even been incorporated into part of a common cliche: Gauge theory is a connection on a principal bundle. We will come back to this relation between physics and geometry in Chapter 14 But just on the geometry side there has been ...
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A Compactification of the Universal Moduli Space of Principal G-Bundles

Mediterranean Journal of Mathematics, 2022
Angel Luis Muñoz Castaneda
exaly