definition 13.27 Riemann symbols

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1383 · p. 467

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 13.25 Second fundamental coefficients ¶
- depends_on definition 13.24 Second fundamental form ¶
  - depends_on definition 13.20 Unit normal vector of a surface ¶
    - depends_on definition 13.19 Parameter curves ¶ ↺
- depends_on definition 13.20 Unit normal vector of a surface ¶ ↺
depends_on equation 13.92 eq:mfd-ecscoda1 ¶

depends_on theorem 13.30 Theorema Egregium; Gauss, 1827 ¶
- depends_on corollary 13.31 Bending invariance ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Christoffel symbols	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1400
`depends_on`	→	Second fundamental coefficients	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1400
`depends_on`	→	eq:mfd-ecscoda1	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1400
`depends_on`	←	Theorema Egregium; Gauss, 1827	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1552