Results 241 to 250 of about 5,433 (284)

Principal Bundles and Connections

2003
The notion of principal bundle as introduced in Section 1.3 is recalled. Invariant vector fields are then introduced as well as the bundle of vertical automorphisms and the bundle of infinitesimal generators of vertical principal automorphisms. Lie derivatives for principal automorphisms and infinitesimal generators of vertical automorphisms are ...
Lorenzo Fatibene, Mauro Francaviglia
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Connections on a Principal Bundle

2020
This chapter discusses connections on a principal bundle. Throughout the chapter, G will be a Lie group with Lie algebra g. One possible definition of a connection on a principal G-bundle P is a C∞ right-invariant horizontal distribution on P. Equivalently, a connection on P can be given by a right-equivariant g-valued 1-form on P that is the identity ...
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PRINCIPAL BUNDLES ADMITTING A HOLOMORPHIC CONNECTION

International Journal of Mathematics, 1996
Let \(G\) be a complex Lie group and \(M\) a compact connected Kähler manifold. Consider \(0={\mathcal E}_0 \subset {\mathcal E}_1 \subset \dots {\mathcal E}_{l-1} \subset {\mathcal E}_l=T\), the Harder-Narasimhan filtration of the holomorphic tangent bundle \(T\) of \(M\). The following result is proven: Theorem.
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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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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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Invariant Connections in a Non-Abelian Principal Bundle

Annals of Physics, 1994
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Hussin, Veronique, Negro, Javier, del Olmo, Mariano A.   +2 more
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Principal bundle, parabolic bundle, and holomorphic connection

2003
Let E G be a principal G—bundle over a rationally connected variety, where G is a complex algebraic group. Then any holomorphic connection on E G is flat. We describe a necessary and sufficient condition for a parabolic vector bundle over a Riemann surface to admit a logarithmic connection compatible with the parabolic structure.
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Universal connections in Fréchet principal bundles

Periodica Mathematica Hungarica, 2007
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Bundle realizations and invariant connections in an Abelian principal bundle

Journal of Mathematical Physics, 1992
In this paper the concept of bundle realization of a Lie group on an Abelian principal bundle is defined. This definition is based on the theory of locally operating realizations of Lie groups. Afterward the bundle realizations are studied and characterized into pseudoequivalence classes.
Negro, Javier, Del Olmo, Mariano A.
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Connections on noncommutative principal bundles

In modern mathematical physics, one is often times concerned with the equations of motion of a certain class of physically representative objects. In field theory over a curved spacetime, these typically take the form of some certain systems of PDEs, such as the Dirac equation (for the electron-positron field).
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