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Holonomy

In differential geometry, the holonomy of a connection on a smooth manifold is the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. Holonomy is a general geometrical consequence of the curvature of the connection. For flat connections, the associated holonomy is a type of monodromy and is an…

Definitions, Riemannian holonomy & Overview

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Overview

Definitions

Ambrose–Singer theorem

Riemannian holonomy

Affine holonomy

Etymology

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Map overview Semantic statistics

Holonomy

Nodes100
Edges99
Triples233
Avg. degree1.98
Density0.02
Components1

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Holonomy

Top relations

related to References · 130
Holonomy → Acad, Académie, Addendum, Advances, Agricola, Amer, American Mathematical Society, André, Ann, Annals, Arch, Armand, Arthur, Astérisque, Berger Holonomy Theorem, Berger's List, Bibcode, Bonan, Borel, Bryant
related to Reducible holonomy and the de Rham decomposition · 13
Holonomy → Allowing, Cartesian, Frobenius, Hol, In, Let, Rham, So, Suppose, The, Then, This, TxM
related to Affine holonomy · 11
Holonomy → Affine, Ambrose, Berger, Berger's, However, Lie, On, Rham, Riemannian, Singer, The
related to Holonomy bundles · 11
Holonomy → As, Furthermore, G-bundle, Hence, Hol, In, Let, The, Then, This, Thus
related to Riemannian holonomy · 10
Holonomy → Borel, In, Levi-Civita, Lichnerowicz, Lie, Manifolds, One, Riemannian, SO, The
related to Ambrose–Singer theorem · 8
Holonomy → In, Levi-Civita, Singer, The, The Ambrose, This, To, WarrenAmbroseandIsadore
related to Etymology · 8
Holonomy → About, Bouquet, Briot, Cauchy's, Golwala, Greek, The, There
related to Holonomy of a connection in a vector bundle · 8
Holonomy → Ex, Given, GL, Hol, Let, Pγ, The, This
related to The Berger classification · 8
Holonomy → Berger, Berger's, Edmond Bonan, In, Manifolds, Riemannian, Sp, Vivian Yoh Kraines
related to Special holonomy and spinors · 7
Holonomy → G2, Hol, If, In, Manifolds, Spin, SU

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Important terminology

connection hol group displaystyle operatorname riemannian manifolds manifold groups omega parallel curvature bundle theorem irreducible connected affine connections symmetric principal

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Holonomyis ageneral geometrical consequence of the curvature of the connection0.90text
Holonomyis atype of monodromy and is an inherently global notion0.90text
Holonomyis atheorem of Borel0.90text
Holonomyrelated to Affine holonomyAffine0.60section
Holonomyrelated to Affine holonomyRiemannian0.60section
Holonomyrelated to Affine holonomyThe0.60section
Holonomyrelated to Affine holonomyRham0.60section
Holonomyrelated to Affine holonomyHowever0.60section
Holonomyrelated to Affine holonomyOn0.60section
Holonomyrelated to Affine holonomyBerger0.60section
Holonomyrelated to Affine holonomyLie0.60section
Holonomyrelated to Affine holonomyBerger's0.60section

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