theorem 14.107 Bianchi identity

open in the book · parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4373 · p. 591

Rests on

depends_on definition 14.105 Curvature $2$-form ¶
- depends_on definition 14.103 Connection $1$-form ¶
  - depends_on definition 14.97 Principal bundle ¶
    - depends_on definition 14.95 Fibre bundle ¶
  - depends_on notation 14.101 Algebra-valued forms and their bracket ¶
- depends_on notation 14.101 Algebra-valued forms and their bracket ¶ ↺
depends_on lemma 14.102 Two identities for a $\mathfrak{g}$-valued $1$-form ¶
- depends_on equation 14.135 eq:lie-form-bracket ¶
- depends_on equation 14.5 eq:lie-structconst ¶
  - step_from equation 14.4 eq:lie-gengrlie ¶
    - step_from equation 14.3 eq:lie-generators ¶
    - step_from equation 14.2 eq:lie-varincor ¶
- proves proof ch:12-lie-groups-fibre-bundles@proof-41 ¶
proves proof ch:12-lie-groups-fibre-bundles@proof-44 ¶

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type	direction	node	provenance	where
`depends_on`	→	Curvature $2$-form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4379
`depends_on`	→	Two identities for a $\mathfrak{g}$-valued $1$-form	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4379
`proves`	←	ch:12-lie-groups-fibre-bundles@proof-44	declared	parts/02-mathematical-methods/12-lie-groups-fibre-bundles.tex:4382