definition 13.24 Second fundamental form
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1103
· p. 463
- ground object -- no derivation owed
Rests on
- depends_on definition 13.20 Unit normal vector of a surface ¶
Supports
-
depends_on
definition 13.25
Second fundamental coefficients
¶
-
depends_on
definition 13.29
Gaussian curvature
¶
-
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
¶
-
depends_on
definition 13.27
Riemann symbols
¶
- depends_on theorem 13.30 Theorema Egregium; Gauss, 1827 ¶ ↺
- depends_on proposition A.493 A harmonic conformal map is a minimal surface ¶
-
depends_on
definition 13.29
Gaussian curvature
¶
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 |
→ | Unit normal vector of a surface | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1111 |
depends_on |
← | Second fundamental coefficients | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1124 |