definition 13.28 Normal curvature vector of a surface
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1411
· p. 467
- ground object -- no derivation owed
Rests on
-
depends_on
definition 13.13
Normal curvature vector of a curve
¶
-
depends_on
definition 13.12
Unit tangent vector
¶
- depends_on definition 13.11 Arc length ¶
- depends_on definition 13.9 Tangent vector to a curve ¶ ↺
-
depends_on
definition 13.12
Unit tangent vector
¶
- depends_on definition 13.20 Unit normal vector of a surface ¶
Supports
-
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 13.36
Geodesic curvature vector
¶
- depends_on definition 13.37 Geodesic lines ¶
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 |
→ | Normal curvature vector of a curve | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1418 |
depends_on |
→ | Unit normal vector of a surface | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1418 |
depends_on |
← | Gaussian curvature | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1525 |
depends_on |
← | Geodesic curvature vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1703 |