definition 13.114 Volume form

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5386 · p. 518

Rests on

depends_on definition 13.117 Metric tensor of signature $(p,q)$ ¶
- depends_on definition 13.48 Differentiable manifold ¶
  - depends_on definition 13.47 Differentiable structure ¶
    - depends_on definition 13.44 Atlas ¶
      - depends_on definition 13.43 Coordinate system ¶
- depends_on definition 13.84 Tensor ¶
  - depends_on definition 13.83 Covector ¶
    - depends_on definition 13.81 Vector on a manifold ¶
      - depends_on definition 13.71 Differentiable curve ¶
      - 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 13.102 Wedge product ¶
- depends_on definition 13.98 $k$-form ¶
  - depends_on definition 13.83 Covector ¶ ↺
  - depends_on definition 13.84 Tensor ¶ ↺
- depends_on equation 13.239 eq:mfd-dual-basis ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Metric tensor of signature $(p,q)$	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5393
`depends_on`	→	Wedge product	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5393
`depends_on`	←	Hodge dual	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5460