definition 13.26 Christoffel symbols

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1213 · p. 465

ground object -- no derivation owed

Rests on

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 13.8 Curve ¶
      - depends_on definition 13.9 Tangent vector to a curve ¶
    - 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 ¶

Supports

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 ¶

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`	→	Inverse metric tensor	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1222
`depends_on`	→	eq:mfd-ecsgauss	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1222
`depends_on`	←	Geodesic lines	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1837
`depends_on`	←	Riemann symbols	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1400