Examples of 'tangent bundle' in a sentence
Meaning of "tangent bundle"
tangent bundle: In mathematics, this phrase defines a geometric structure that associates each point on a manifold with a tangent space at that point, resulting in a smooth vector bundle
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- A fiber bundle for which the base space is a differentiable manifold and each fiber over a point of that manifold is the tangent space of that point.
How to use "tangent bundle" in a sentence
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tangent bundle
This is equivalent to the tangent bundle being trivial.
Use of microbundles allows the definition of a topological tangent bundle.
An example is the tangent bundle of a smooth variety over a field.
It may be described also as the dual bundle to the tangent bundle.
The unit tangent bundle carries a variety of differential geometric structures.
The natural projection on the tangent bundle on a manifold.
Orientability and orientations can also be expressed in terms of the tangent bundle.
Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.
The geodesic flow defines a family of curves in the tangent bundle.
For example, consider the tangent bundle TSn for n even.
A local vector field on M is a local section of the tangent bundle.
The tangent bundle is where tangent vectors lie, and is itself a differentiable manifold.
The Lagrangian is a function on the tangent bundle.
For example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem.
Sasaki metric a natural choice of Riemannian metric on the tangent bundle of Riemannian manifold.
See also
Liouville 's theorem implies invariance of a kinematic measure on the unit tangent bundle.
This action is conjugate to a frame flow on the tangent bundle of an hyperbolic 3-manifold.
Unlike the 2-sphere, the 3-sphere admits nonvanishing vector fields sections of its tangent bundle.
Sprays and connections on the tangent bundle of order 2.
The Finsler metric is a continuous nonnegative function F, TM → 0, + ∞ defined on the tangent bundle.
If M is an almost complex manifold, then its tangent bundle is a complex vector bundle.
More specifically, a vector field can mean a section of the tangent bundle.
It follows that the tangent bundle of the 3-sphere is trivial.
Tangent field, a section of the tangent bundle.
For 2-dimensional manifolds the tangent bundle is 4-dimensional and hence difficult to visualize.
In Riemannian geometry, the Levi-Civita connection is a specific connection on the tangent bundle of a manifold.
In the first part, we study varieties ( mostly surfaces ) whose tangent bundle is pseudo-effective.
By definition, a manifold M { \ displaystyle M } is parallelizable if and only if the tangent bundle is trivial.
Distribution ( differential geometry ), a subset of the tangent bundle of a manifold.
Example 1, D = - i ∂ x is a Dirac operator on the tangent bundle over a line.
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Examples of using Tangent
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Provides the tangent arc of a real value
Tangent line to the graph of a function at a point
We took the tangent to the central area
Examples of using Bundle
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I will make a bundle selling them at school
Bundle yourself up and speak to the wind
We could save a bundle on her insurance premiums
