example 13.87 The $2$-sphere

Rests on

• depends_on definition 13.82 Vector field ¶
  • depends_on definition 13.81 Vector on a manifold ¶
    • depends_on definition 13.71 Differentiable curve ¶
      • depends_on definition 13.48 Differentiable manifold ¶
        • depends_on definition 13.47 Differentiable structure ¶
    • depends_on definition 13.45 Differentiable map on a topological space ¶
      • depends_on definition 13.44 Atlas ¶
        • depends_on definition 13.43 Coordinate system ¶
      • depends_on definition 13.43 Coordinate system ¶ ↺
    • depends_on definition 13.48 Differentiable manifold ¶ ↺
• depends_on definition 13.81 Vector on a manifold ¶ ↺
• depends_on example 13.61 The $2$-sphere in $\R^{3}$ ¶
  • 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 6.7 Homeomorphism ¶
      • depends_on definition 13.48 Differentiable manifold ¶ ↺
  • 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 ¶
      • depends_on definition 13.44 Atlas ¶ ↺
      • depends_on definition 13.45 Differentiable map on a topological space ¶ ↺
      • depends_on definition 13.48 Differentiable manifold ¶ ↺
    • proves proof ch:11-manifolds-tensors-curvature@proof-10 ¶

Supports

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