equation A.972 eq:app-adm-gauss-codazzi-projector

open in the book · appendices/A-long-proofs.tex:30169

part of a statement or proof

Rests on

No declared or derived dependency edges point away from this node yet.

Supports

depends_on definition A.625 Four-dimensional extrinsic curvature ¶
- 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.626 Decomposition of $\nabla n$, and the acceleration ¶
  - depends_on lemma A.630 Codazzi equation ¶ ↺
  - depends_on lemma A.631 The normal–normal Ricci contraction ¶
    - depends_on theorem A.632 The $3+1$ identity for the curvature scalar ¶ ↺

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`	←	Four-dimensional extrinsic curvature	declared	appendices/A-long-proofs.tex:30222