equation 13.305 eq:mfd-ricci-identity

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6682

part of a statement or proof

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Supports

depends_on lemma A.630 Codazzi equation ¶
- depends_on theorem 44.42 The constraint equations ¶
  - depends_on theorem 44.45 Local existence and uniqueness; Choquet-Bruhat; imported ¶
    - depends_on theorem 44.46 Maximal globally hyperbolic development; Choquet-Bruhat and Geroch; imported ¶
  - depends_on theorem 44.46 Maximal globally hyperbolic development; Choquet-Bruhat and Geroch; imported ¶ ↺
depends_on lemma A.628 Gauss equation, arbitrary signature ¶
- depends_on theorem A.632 The $3+1$ identity for the curvature scalar ¶
- depends_on theorem 44.42 The constraint equations ¶ ↺
depends_on lemma A.631 The normal–normal Ricci contraction ¶
- depends_on theorem A.632 The $3+1$ identity for the curvature scalar ¶ ↺

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Edges

type	direction	node	provenance	where
`depends_on`	←	Codazzi equation	declared	appendices/A-long-proofs.tex:30506
`depends_on`	←	Gauss equation, arbitrary signature	declared	appendices/A-long-proofs.tex:30400
`depends_on`	←	The normal–normal Ricci contraction	declared	appendices/A-long-proofs.tex:30581