Results 331 to 340 of about 2,005,987 (380)
Some of the next articles are maybe not open access.
On the Grothendieck-Serre Conjecture about principal bundles and its generalizations
, 2018Let $U$ be a regular connected semi-local scheme over a field $k$. Let $G$ be a reductive group scheme over $U$. Then a principal $G$-bundle over $U$ is trivial, if it is rationally trivial. We give a direct proof of this statement without reducing first
R. Fedorov
semanticscholar +1 more source
Sbornik: Mathematics, 1999
The class A of bundles with the following properties is investigated: each bundle in A is the composition of a regular cover and a principal bundle (over the covering space) with Abelian structure group; the standard fibre G of this decomposable bundle is a Lie group; the bundle has an atlas with multivalued transition functions taking values in the ...
openaire +2 more sources
The class A of bundles with the following properties is investigated: each bundle in A is the composition of a regular cover and a principal bundle (over the covering space) with Abelian structure group; the standard fibre G of this decomposable bundle is a Lie group; the bundle has an atlas with multivalued transition functions taking values in the ...
openaire +2 more sources
Noncommutative Principal Bundles Through Twist Deformation
, 2016We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the fibers.
P. Aschieri +3 more
semanticscholar +1 more source
HARMONIC MAPS AND BIHARMONIC MAPS ON PRINCIPAL BUNDLES AND WARPED PRODUCTS
, 2018. In this paper, we study harmonic maps and biharmonic maps on the principal G -bundle in Kobayashi and Nomizu [22] and also the warped product P = M × f F for a C ∞ ( M ) function f on M studied by Bishop and O’Neill [4], and Ejiri [11].
H. Urakawa
semanticscholar +1 more source
Archiv der Mathematik, 2007
Let T be a complex torus and E T a holomorphic principal T-bundle over a connected complex manifold M. We prove that the total space of E T admits a Kahler structure if and only if M admits a Kahler structure and E T admits a flat holomorphic ...
openaire +2 more sources
Let T be a complex torus and E T a holomorphic principal T-bundle over a connected complex manifold M. We prove that the total space of E T admits a Kahler structure if and only if M admits a Kahler structure and E T admits a flat holomorphic ...
openaire +2 more sources
Connections on Principal Bundles
2015The 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 ...
openaire +2 more sources
2015
The importance of the role of principal fiber bundles in classical differential geometry and physics is well established. We now consider the generalization of this structure in the context of noncommutative geometry. The material in this chapter is based on several of Micho Ðurđevich’s papers (see especially [22] and [26] but also [21] and [23]).
openaire +2 more sources
The importance of the role of principal fiber bundles in classical differential geometry and physics is well established. We now consider the generalization of this structure in the context of noncommutative geometry. The material in this chapter is based on several of Micho Ðurđevich’s papers (see especially [22] and [26] but also [21] and [23]).
openaire +2 more sources
Connections on a Principal Bundle
2020This 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 ...
openaire +1 more source
Curvature on a Principal Bundle
2020This chapter examines curvature on a principal bundle. The curvature of a connection on a principal G-bundle is a g-valued 2-form that measures, in some sense, the deviation of the connection from the Maurer-Cartan connection on a product bundle. The Maurer-Cartan form Θ on a Lie group G satisfies the Maurer-Cartan equation. Let M be a smooth manifold.
openaire +1 more source
1979
A principal bundle E over a space X ( or a G-bundle, for short ) is a space E onwhich G operates (from the right ) and a G-invariant morphism p: E ~ X which is locally trivial in the etale topology, i.e. for every point x of X there is a neighbourhood U of x and an etale covering f: U' ~ U such that there is a G-equivariant isomorphism of f(E) with U'x
openaire +2 more sources
A principal bundle E over a space X ( or a G-bundle, for short ) is a space E onwhich G operates (from the right ) and a G-invariant morphism p: E ~ X which is locally trivial in the etale topology, i.e. for every point x of X there is a neighbourhood U of x and an etale covering f: U' ~ U such that there is a G-equivariant isomorphism of f(E) with U'x
openaire +2 more sources