Examples of 'smooth manifold' in a sentence
Meaning of "smooth manifold"
smooth manifold ~ a mathematical term describing a type of mathematical object that is both a manifold and has a smooth structure, often used in the field of differential geometry
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- A manifold which is infinitely differentiable (C ᪲).
How to use "smooth manifold" in a sentence
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smooth manifold
A hypersurface that is a smooth manifold is called a smooth hypersurface.
Pontryagin numbers are certain topological invariants of a smooth manifold.
A smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space.
They are topological invariants associated to vector bundles on a smooth manifold.
Suppose that M is a smooth manifold containing a point pp.
This construction is in particular applied to the cotangent bundle of a smooth manifold.
Any smooth manifold admits a Riemannian metric, which often helps to solve problems of differential topology.
They are topological invariants associated with vector bundles on a smooth manifold.
A smooth manifold or C∞-manifold is a differentiable manifold for which all the transition maps are smooth.
It is true that every complex manifold is in particular a real smooth manifold.
This gives a three-dimensional smooth manifold which becomes a Riemannian manifold when we add the metric structure.
The same criterion holds more generally for diffeomorphisms of a smooth manifold.
Abstract, A Poisson structure defined on a smooth manifold induces a foliation by symplectic leaves.
Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold.
Let M be a connected paracompact smooth manifold and P a principal G-bundle with connection ω, as above.
See also
But if the stabilizer groups change we can not expect a smooth manifold any longer.
Every smooth manifold is a ( topological ) manifold.
The tangent space of an n-dimensional smooth manifold at the point.
Any smooth manifold of dimension " n " ≥ 3 admits a Riemannian metric with negative Ricci curvature.
A world manifold is a four-dimensional orientable real smooth manifold.
Curved spaces ===A smooth manifold is a Hausdorff topological space that is locally diffeomorphic to Euclidean space.
Mathematically, spacetime symmetries are usually described by smooth vector fields on a smooth manifold.
Local feature size for a smooth manifold ( black ) with medial axis ( red ).
As the transition map is a smooth function, this atlas defines a smooth manifold.
Smooth ( differentiable ) functions, paths, maps, given in a smooth manifold by definition, lead to tangent spaces.
A smooth plane curve is a curve in a real Euclidean plane R2 and is a one-dimensional smooth manifold.
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Examples of using Smooth
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Smooth movements and moments of chaos alternate
You are not as smooth as you think you are
Smooth how you slid that in there
