definition 13.122 Vielbein

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5589 · p. 521

ground object -- no derivation owed

Rests on

depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on definition 13.48 Differentiable manifold ¶
  - depends_on definition 13.47 Differentiable structure ¶
    - depends_on definition 13.44 Atlas ¶
      - depends_on definition 13.43 Coordinate system ¶
- depends_on definition 13.84 Tensor ¶
  - depends_on definition 13.83 Covector ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - depends_on definition 13.45 Differentiable map on a topological space ¶
      - depends_on definition 13.48 Differentiable manifold ¶ ↺
  - depends_on definition 13.81 Vector on a manifold ¶ ↺
depends_on equation 13.1 eq:mfd-eta ¶

Supports

depends_on proposition 13.123 Local Lorentz freedom ¶
- depends_on theorem A.49 thm:app-eh-equivalence ¶
depends_on theorem 43.3 Equivalence of the two variable sets ¶
- depends_on proposition 44.13 First-order variation in vielbein-form variables ¶
depends_on theorem 13.156 Cartan structure equations ¶
- depends_on proposition 44.13 First-order variation in vielbein-form variables ¶ ↺
- depends_on proposition 13.157 Bianchi identities ¶
  - depends_on proposition 13.154 Symmetries of the curvature ¶
    - depends_on definition 13.111 Linearised curvature of a symmetric field ¶
      - depends_on theorem 13.112 Symmetric analogue of the converse Poincaré lemma ¶
    - depends_on theorem 44.23 Contracted Bianchi identity ¶
      - depends_on corollary 44.24 Conservation is an integrability condition ¶
      - depends_on proposition 44.41 Four of the ten equations are constraints ¶
      - depends_on proposition 44.30 The cosmological term ¶
      - depends_on theorem 44.33 Lovelock's uniqueness theorem; imported ¶
    - depends_on theorem 13.160 Maximal symmetry forces constant curvature ¶
      - depends_on proposition 44.31 de Sitter geometry ¶
      - depends_on proposition 15.31 Radius and cosmological constant ¶
      - depends_on theorem 48.3 The Robertson–Walker metric ¶
- depends_on proposition 13.158 The connection determined by vielbein and torsion ¶
  - depends_on proposition 44.13 First-order variation in vielbein-form variables ¶ ↺
  - depends_on theorem 43.3 Equivalence of the two variable sets ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Metric tensor of signature $(p,q)$	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5604
`depends_on`	→	eq:mfd-eta	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5604
`depends_on`	←	Local Lorentz freedom	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5617
`depends_on`	←	Equivalence of the two variable sets	declared	parts/05-general-relativity-cosmology/02-geometric-formulation.tex:193
`depends_on`	←	Cartan structure equations	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6841