definition 13.23 Inverse metric tensor
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1011
· p. 462
- ground object -- no derivation owed
Rests on
-
depends_on
definition 13.22
First fundamental coefficients
¶
-
depends_on
definition 13.21
First fundamental form
¶
- depends_on definition 13.11 Arc length ¶
- depends_on definition 13.18 Surface ¶
- depends_on definition 13.19 Parameter curves ¶
-
depends_on
definition 13.21
First fundamental form
¶
Supports
-
depends_on
definition 13.26
Christoffel symbols
¶
- depends_on definition 13.37 Geodesic lines ¶
-
depends_on
definition 13.27
Riemann symbols
¶
-
depends_on
theorem 13.30
Theorema Egregium; Gauss, 1827
¶
- depends_on corollary 13.31 Bending invariance ¶
-
depends_on
theorem 13.30
Theorema Egregium; Gauss, 1827
¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | First fundamental coefficients | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1017 |
depends_on |
← | Christoffel symbols | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1222 |