example 13.61 The $2$-sphere in $\R^{3}$

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2825 · p. 486

Rests on

depends_on definition 13.58 Hypersurface ¶
- 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 13.81 Vector on a manifold ¶
    - depends_on definition 6.7 Homeomorphism ¶
      - depends_on definition 3.47 Bijective map ¶
      - depends_on definition 3.51 Inverse map ¶
      - depends_on definition 6.6 Continuous map ¶
  - depends_on definition 13.48 Differentiable manifold ¶
    - depends_on definition 13.47 Differentiable structure ¶
      - depends_on definition 13.44 Atlas ¶
depends_on theorem 13.59 Regular value theorem ¶
- depends_on definition 13.52 Differential; pushforward ¶ ↺
- depends_on definition 13.58 Hypersurface ¶ ↺
- depends_on definition 13.49 Smooth map between manifolds ¶ ↺
- proves proof ch:11-manifolds-tensors-curvature@proof-10 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Hypersurface	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2850
`depends_on`	→	Regular value theorem	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:2850
`depends_on`	←	The sphere, made explicit	declared	appendices/A-long-proofs.tex:14775
`depends_on`	←	The $2$-sphere	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:4203