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Christoffel symbols

In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without…

Applications, Preliminary definitions & General definition

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Overview

Preliminary definitions

Definition in Euclidean space

General definition

Transformation law under change of variable

Relationship to parallel transport and derivation of Christoffel symbols in Riemannian space

Relationship to index-free notation

Covariant derivatives of tensors

Applications

Lagrangian mechanics in geodesics (principles of least action in Christoffel symbols)

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Map overview Semantic statistics

Christoffel symbols

Nodes109
Edges108
Triples54
Avg. degree1.98
Density0.018349
Components1

How this topic connects Entity context

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Christoffel symbols

Top relations

related to Christoffel symbols of the second kind (symmetric definition) · 8
Christoffel symbols → Christoffel, For, Gamma, Hence, In, Levi-Civita, Since, The Christoffel
related to In general relativity · 8
Christoffel symbols → Christoffel, Einstein's, Levi-Civita, Lorentz, Once, Ricci, The Christoffel, The Einstein
related to Lagrangian mechanics in geodesics (principles of least action in Christoffel symbols) · 7
Christoffel symbols → Christoffel, Euler, Euler-Lagrange, Incorporating Lagrangian, Lagrange, Lagrangian, When
related to Relationship to parallel transport and derivation of Christoffel symbols in Riemannian space · 6
Christoffel symbols → Christoffel, Gamma, If, Now, Riemannian, The
related to Connection coefficients in a nonholonomic basis · 5
Christoffel symbols → Christoffel, Explicitly, However, In, The Christoffel
related to Note · 5
Christoffel symbols → Christoffel, Einstein, Levi-Civita, Riemannian, The
see also · 4
Christoffel symbols → Christoffel, Codazzi, Introduction, Riemannian
related to Christoffel symbols of the first kind · 3
Christoffel symbols → Christoffel, Gamma, The Christoffel
related to Definition in Euclidean space · 3
Christoffel symbols → Christoffel, Gamma, In Euclidean
related to Transformation law under change of variable · 3
Christoffel symbols → Christoffel, Gamma, Under

Important terminology Word statistics

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Important terminology

displaystyle christoffel tensor symbols metric basis gamma partial coordinate connection frac manifold general covariant coordinates vectors given indices notation ik

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Christoffel symbolsrelated to Christoffel symbols of the first kindThe Christoffel0.60section
Christoffel symbolsrelated to Christoffel symbols of the first kindChristoffel0.60section
Christoffel symbolsrelated to Christoffel symbols of the first kindGamma0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)The Christoffel0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)Levi-Civita0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)In0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)Christoffel0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)Gamma0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)Since0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)Hence0.60section
Christoffel symbolsrelated to Christoffel symbols of the second kind (symmetric definition)For0.60section
Christoffel symbolsrelated to Connection coefficients in a nonholonomic basisThe Christoffel0.60section

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