Results 31 to 40 of about 226,986 (311)
The Existence of Cartan Connections and Geometrizable Principal Bundles [PDF]
Arch. Math. (Basel) 83 (2004), no. 2, 159-163, 2002 The aim of this article is to proof a necessary and sufficient condition for the existence of a Cartan connection on a principal bundle. After collecting the essentially well known facts to fix the terminology, soldering forms and geometrizable principal bundles are defined to finally prove the existence criterion.
arxiv +5 more sources
A global perspective to connections on principal 2-bundles [PDF]
Forum Mathematicum, 2016 Abstract For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids.
Konrad Waldorf
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A Discrete Theory of Connections on Principal Bundles
, 2005 Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the
Melvin Leok +2 more
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Equivariant principal bundles for G–actions and G–connections
Complex Manifolds, 2015 Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection.
Biswas Indranil +2 more
doaj +3 more sources
Functoriality of Quantum Principal Bundles and Quantum Connections
, 2020 The purpose of this work is to present a complet categorical point of view of the association between finite dimmensional representations of a compact quantum group and quantum vector bundles with quantum linear connections using M. Durdevichs theory.
Gustavo Amilcar Saldaña Moncada
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Discrete connections on principal bundles: abelian group case
, 2021 In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature can be interpreted as singular $1$ and $2$ cochains respectively, with the curvature being the coboundary of the ...
Javier Fernández +2 more
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Linear and projective connections over a smooth manifold
Дифференциальная геометрия многообразий фигур, 2023 The principal bundles of the first order coframes and the second order coframes, as well as factor bundle of centroprojective (coaffine) coframes are considered.
Yu. I. Shevchenko, A. V. Vyalova
doaj +1 more source
Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory
Axioms, 2021 Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature measures the “instantaneous arbitrage capability”.
Simone Farinelli, Hideyuki Takada
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Glued linear connection on surface of the projective space
Дифференциальная геометрия многообразий фигур, 2020 We consider a surface as a variety of centered planes in a multidimensional projective space. A fiber bundle of the linear coframes appears over this manifold. It is important to emphasize the fiber bundle is not the principal bundle.
K.V. Bashashina
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, 2020 We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two restricting ...
J. François
semanticscholar +1 more source