Examples of 'vector bundle' in a sentence
Meaning of "vector bundle"
vector bundle ~ In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
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- A fiber bundle for which the fiber is a vector space.
How to use "vector bundle" in a sentence
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vector bundle
Every vector bundle admits a connection.
This is sometimes taken as the definition of a vector bundle.
Secondary vector bundle structure.
Holonomy of a connection in a vector bundle.
Vector bundle homomorphism.
Holomorphic vector bundle.
Vector bundle morphism.
Hermitian vector bundle.
This subsection deals with the notion of jets of local sections of a vector bundle.
Rank of a vector bundle.
A Koszul connection is a connection generalizing the derivative in a vector bundle.
Real vector bundle.
Vector field, a section of a vector bundle.
Complex vector bundle.
Any vector bundle associated to E can be given by the above construction.
See also
Tangent vector bundle.
Let be a base space, and let be a real vector bundle.
The definition of a vector bundle shows that any vector bundle is locally trivial.
Connection on a vector bundle.
Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.
More generally, a similar approach applies for connections in any vector bundle.
The basic invariant of a complex vector bundle is a Chern class.
If M is an almost complex manifold, then its tangent bundle is a complex vector bundle.
In mathematics, a complex vector bundle is a vector bundle whose fibers are complex vector spaces.
More generally, any vector bundle.
On the other hand, a vector bundle always has a global section, namely the zero section.
Like other characteristic classes, it measures how " twisted " the vector bundle is.
Thirdly, we develop a theoretical framework for vector bundle filtrations, and define the persistent Stiefel-Whitney classes.
However, the same property holds for any ( Koszul or linear Ehresmann ) connection on a vector bundle.
A complex vector bundle is canonically oriented ; in particular, one can take its Euler class.
For concreteness, suppose that ( E, g ) is a Riemannian vector bundle.
A real vector bundle consists of,.
Every vector bundle theory ( real, complex etc . ) has an extraordinary cohomology theory called K-theory.
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