definition 13.130 Distribution; involutive; integrable

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5913 · p. 524

Rests on

depends_on definition 13.54 Embedded submanifold ¶
- depends_on definition 13.53 Immersion, submersion, embedding ¶
  - depends_on definition 13.52 Differential; pushforward ¶
    - depends_on definition 13.49 Smooth map between manifolds ¶
      - depends_on definition 13.44 Atlas ¶
      - 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 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 6.7 Homeomorphism ¶
    - depends_on definition 3.47 Bijective map ¶
    - depends_on definition 3.51 Inverse map ¶
      - depends_on definition 3.47 Bijective map ¶ ↺
      - depends_on definition 3.49 Composition map ¶
      - depends_on definition 3.50 Identity map ¶
    - depends_on definition 6.6 Continuous map ¶
      - depends_on definition 3.53 Preimage ¶
      - depends_on definition 6.2 Open set ¶
      - depends_on definition 6.1 Topological space ¶
- depends_on definition 13.48 Differentiable manifold ¶ ↺
depends_on definition 13.82 Vector field ¶
- depends_on definition 13.81 Vector on a manifold ¶ ↺
depends_on equation 13.273 eq:mfd-lie-vector ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Embedded submanifold	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5929
`depends_on`	→	Vector field	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5929
`depends_on`	→	eq:mfd-lie-vector	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5929
`depends_on`	←	Frobenius for a Pfaffian system	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6114
`depends_on`	←	Frobenius	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:6030