definition 13.116 Hodge dual
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5449
· p. 519
- ground object -- no derivation owed
Rests on
-
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 13.71
Differentiable curve
¶
- depends_on definition 13.48 Differentiable manifold ¶
-
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 13.48 Differentiable manifold ¶ ↺
-
depends_on
definition 13.71
Differentiable curve
¶
-
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 13.83
Covector
¶
-
depends_on
definition 13.99
$k$-vector
¶
- depends_on definition 13.84 Tensor ¶ ↺
- depends_on definition 13.81 Vector on a manifold ¶ ↺
-
depends_on
definition 13.114
Volume form
¶
-
depends_on
definition 13.117
Metric tensor of signature $(p,q)$
¶
- depends_on definition 13.48 Differentiable manifold ¶ ↺
- depends_on definition 13.84 Tensor ¶ ↺
-
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 13.117
Metric tensor of signature $(p,q)$
¶
Supports
Nothing declares a dependency on this node yet.
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
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- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | $k$-form | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5460 |
depends_on |
→ | $k$-vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5460 |
depends_on |
→ | Volume form | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:5460 |