definition 13.37 Geodesic lines

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1824 · p. 473

ground object -- no derivation owed

Rests on

depends_on definition 13.26 Christoffel symbols ¶
- depends_on definition 13.23 Inverse metric tensor ¶
  - 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 13.8 Curve ¶
      - depends_on definition 13.18 Surface ¶ ↺
- depends_on equation 13.83 eq:mfd-ecsgauss ¶
depends_on definition 13.36 Geodesic curvature vector ¶
- 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 13.8 Curve ¶ ↺
- depends_on definition 13.28 Normal curvature vector of a surface ¶
  - depends_on definition 13.13 Normal curvature vector of a curve ¶ ↺
  - depends_on definition 13.20 Unit normal vector of a surface ¶
    - depends_on definition 13.19 Parameter curves ¶ ↺
- depends_on definition 13.35 Projection curve ¶
depends_on equation 13.120 eq:mfd-kg-expr ¶

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
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Christoffel symbols	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1837
`depends_on`	→	Geodesic curvature vector	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1837
`depends_on`	→	eq:mfd-kg-expr	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1837