Examples of 'differentiable manifold' in a sentence
Meaning of "differentiable manifold"
differentiable manifold - In mathematics, a differentiable manifold is a space that is locally similar to Euclidean space, but may have a more complex global structure. It is a key concept in differential geometry and calculus, used to study smooth and continuous functions on various spaces
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- A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus; (more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
- A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;
- a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
How to use "differentiable manifold" in a sentence
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differentiable manifold
Similarly for a differentiable manifold it has to be a diffeomorphism.
A volume form provides a means to define the integral of a function on a differentiable manifold.
Noncommutative differentiable manifold.
Any differentiable manifold can be given a Riemannian structure.
Another way to define orientations on a differentiable manifold is through volume forms.
Riemannian metric, a type of metric function that is appropriate to impose on any differentiable manifold.
Orientable differentiable manifold.
The most intuitive definitions require that M be a differentiable manifold.
Every paracompact differentiable manifold admits a Riemannian metric.
Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.
A Ck manifold is a differentiable manifold whose chart overlap functions are k times continuously differentiable.
Let M be a paracompact differentiable manifold.
An n-dimensional differentiable manifold is a generalisation of n-dimensional Euclidean space.
The tangent bundle is where tangent vectors lie, and is itself a differentiable manifold.
A frame at a point of a differentiable manifold M is a basis of the tangent space at the point.
See also
Integration is a kind of " summation " over a continuum, or more precisely and generally, over a differentiable manifold.
An automorphism of a differentiable manifold M is a diffeomorphism from M to itself.
In contemporary differential geometry, a " surface ", viewed abstractly, is a two-dimensional differentiable manifold.
Let M be a compact differentiable manifold.
Let M be a differentiable manifold that is second-countable and Hausdorff.
Let S { \ displaystyle S } be an orientable smooth surface ( a differentiable manifold of dimension 2 ).
In differential geometry, a differentiable manifold is a space where each neighborhood is diffeomorphic to Euclidean space.
The space of Riemannian metrics on a given differentiable manifold is an infinite-dimensional space.
An exotic R4 is a differentiable manifold that is homeomorphic but not diffeomorphic to the Euclidean space R4.
In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle.
In differential geometry, an affine manifold is a differentiable manifold equipped with a flat, torsion-free connection.
A smooth manifold or C∞-manifold is a differentiable manifold for which all the transition maps are smooth.
Differentiable may refer to: Differentiable function Differentiable manifold Differentiable stack Differentiable neural computer.
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Examples of using Differentiable
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Similarly for a differentiable manifold it has to be a diffeomorphism
Harmonic functions are infinitely differentiable in open sets
Differentiable and holomorphic functions of a complex variable
