definition 13.13 Normal curvature vector of a curve
open in the book ·
parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:701
· p. 458
- ground object -- no derivation owed
Rests on
-
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 ¶ ↺
Supports
-
depends_on
definition 13.36
Geodesic curvature vector
¶
- depends_on definition 13.37 Geodesic lines ¶
-
depends_on
definition 13.28
Normal curvature vector of a surface
¶
-
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 13.29
Gaussian curvature
¶
-
depends_on
definition 13.14
Principal unit normal vector
¶
- depends_on definition 13.15 Unit binormal vector ¶
-
depends_on
proposition 18.33
Intrinsic decomposition of the acceleration
¶
- depends_on remark 18.34 The two ways an acceleration can be zero ¶
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 tangent vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:706 |
depends_on |
← | Geodesic curvature vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1703 |
depends_on |
← | Normal curvature vector of a surface | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1418 |
depends_on |
← | Principal unit normal vector | declared | parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:732 |