example 13.110 Closed but not exact: the angle form

Rests on

• depends_on definition 13.106 Exact form ¶
  • depends_on definition 13.103 Exterior derivative ¶
    • depends_on definition 13.98 $k$-form ¶
      • depends_on definition 13.83 Covector ¶
        • depends_on definition 13.81 Vector on a manifold ¶
      • depends_on definition 13.84 Tensor ¶
        • depends_on definition 13.83 Covector ¶ ↺
        • depends_on definition 13.81 Vector on a manifold ¶ ↺
    • depends_on definition 13.102 Wedge product ¶
      • depends_on definition 13.98 $k$-form ¶ ↺
      • depends_on equation 13.239 eq:mfd-dual-basis ¶
  • depends_on definition 13.98 $k$-form ¶ ↺
• depends_on theorem 13.109 Converse of the Poincaré lemma on a star-shaped domain ¶
  • depends_on definition 13.105 Closed form ¶
    • depends_on definition 13.103 Exterior derivative ¶ ↺
    • depends_on definition 13.98 $k$-form ¶ ↺
  • depends_on definition 13.106 Exact form ¶ ↺
  • depends_on definition 13.108 Star-shaped domain ¶
    • depends_on definition 6.2 Open set ¶
      • depends_on definition 6.1 Topological space ¶
        • depends_on definition 3.31 Empty set ¶
        • depends_on definition 3.35 Union, intersection, difference ¶
        • depends_on definition 3.30 Subset ¶
        • depends_on equation 3.51 eq:set-indexed ¶
    • depends_on equation 6.12 eq:top-euclidean-metric ¶
  • proves proof ch:11-manifolds-tensors-curvature@proof-22 ¶

Supports

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