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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a…

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Overview

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Definition

Differentiable functions

Bundles

Calculus on manifolds

Topology of differentiable manifolds

Structures on smooth manifolds

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Differentiable manifold

Nodes228
Edges227
Triples90
Avg. degree1.99
Density0.008772
Components1

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Differentiable manifold

Top relations

related to Differential calculus of functions · 12
Differentiable manifold → At, Differentiable, Functions, However, If, It, Sard's, Tf, The, TM, TN, Usually
related to Differentiability of mappings between manifolds · 11
Differentiable manifold → But, Ck, Euclidean, However, If, Once, Rm, Rn, Since, Suppose, We
related to Calculus on manifolds · 9
Differentiable manifold → Euclidean, For, From, In, Many, One, Several, The, There
related to Manifolds · 9
Differentiable manifold → By, C0, Given, Hausdorff, However, It, Much, The, They
related to Structure sheaf · 9
Differentiable manifold → Ck, Ck-structure, Here, In, Instead, Rn, Sometimes, The, Thus
related to Partitions of unity · 7
Differentiable manifold → Ck, Let, One, Suppose, Then, This, Uα
related to Tangent bundle · 7
Differentiable manifold → Each, For, One, Rn, The, The Lagrangian, Uα
related to Cotangent bundle · 5
Differentiable manifold → Cotangent, Like, One, The, The Hamiltonian
related to Differentiable functions · 4
Differentiable manifold → Analogous, Ck, In, It
related to Tensor bundle · 4
Differentiable manifold → Each, It, Sometimes, The

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Important terminology

manifold differentiable space displaystyle one atlas smooth differential functions tangent manifolds vector structure topological derivative given bundle rn function chart

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Differentiable manifoldis atopological manifold with a globally defined differential structure0.90text
Differentiable manifoldis aHausdorff and second countable topological space M0.90text
classical mechanicsinstance ofSpecial kinds of differentiable manifolds form the basis for physical theories0.80text
general relativityinstance ofSpecial kinds of differentiable manifolds form the basis for physical theories0.80text
and Yanginstance ofSpecial kinds of differentiable manifolds form the basis for physical theories0.80text
James Clerk Maxwellinstance ofRiemannThe works of physicists0.80text
and mathematicians Gregorio Ricci-Curbastroinstance ofRiemannThe works of physicists0.80text
Tullio Levi-Civita led to the development of tensor analysisinstance ofRiemannThe works of physicists0.80text
the notion of covarianceinstance ofRiemannThe works of physicists0.80text
which identifies an intrinsic geometric property as one that is invariant with respect to coordinate transformationsinstance ofRiemannThe works of physicists0.80text
Differentiable manifoldrelated to Calculus on manifoldsMany0.60section
Differentiable manifoldrelated to Calculus on manifoldsOne0.60section

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