proposition 13.163 Integration of the conformal Killing equation
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7268
· p. 538
Rests on
-
depends_on
definition 13.139
Killing vector
¶
-
depends_on
definition 13.120
Isometry
¶
-
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 13.84
Tensor
¶
- depends_on definition 13.83 Covector ¶
- depends_on definition 13.81 Vector on a manifold ¶
-
depends_on
definition 13.48
Differentiable manifold
¶
-
depends_on
definition 13.117
Metric tensor of signature $(p,q)$
¶
- depends_on equation 13.267 eq:mfd-lie-def ¶
-
depends_on
definition 13.120
Isometry
¶
- depends_on equation 13.333 eq:mfd-conformal-killing ¶
- depends_on equation 13.275 eq:mfd-lie-metric ¶
- proves proof ch:11-manifolds-tensors-curvature@proof-50 ¶
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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- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Killing vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7279 |
depends_on |
→ | eq:mfd-conformal-killing | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7279 |
depends_on |
→ | eq:mfd-lie-metric | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7279 |
proves |
← | ch:11-manifolds-tensors-curvature@proof-50 | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:7282 |