Results 281 to 290 of about 4,482,002 (322)

The Principal Floquet Bundle and Exponential Separation for Linear Parabolic Equations

Journal of Dynamics and Differential Equations, 2004
Peter Poláčik
exaly   +2 more sources

Chern Correspondence for Higher Principal Bundles

Communications in Mathematical Physics, 2023
The classical Chern correspondence states that a choice of Hermitian metric on a holomorphic vector bundle determines uniquely a unitary ‘Chern connection’. We generalize the Chern correspondence to the context of higher gauge theory, where the structure
Roberto Tellez-Dominguez
semanticscholar   +1 more source

Coverings in the Category of Principal Bundles

Russian Mathematics, 2021
The main object of this paper is to study regular coverings in the category of smooth principal bundles \(\xi = (E, p, B, G)\) with connected bases \(B\) and structural groups \(G\). A smooth principal bundle is a quadruple \(\xi = (E, p, B, G)\), where \(E\) and \(B\) are smooth manifolds, \(p\colon E \rightarrow B\) is a smooth mapping, and \(G\) is ...
Gonchar, T. A., Yakovlev, E. I.
openaire   +1 more source

Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field

Izvestiya: Mathematics, 2020
Let be a regular local ring containing a field. Let be a reductive group scheme over . We prove that a principal -bundle over is trivial if it is trivial over the field of fractions of .
I. Panin
semanticscholar   +1 more source

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

ON GROTHENDIECK–SERRE CONJECTURE CONCERNING PRINCIPAL BUNDLES

International Congress of Mathematicans, 2019
Let R be a regular local ring. Let G be a reductive group scheme over R. A wellknown conjecture due to Grothendieck and Serre assertes that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the
I. Panin
semanticscholar   +1 more source

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.
openaire   +2 more sources

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 ...
openaire   +1 more source

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.
openaire   +1 more source

Covariant and dynamical reduction for principal bundle field theories

, 2008
M. Castrillón López, J. Marsden
semanticscholar   +1 more source