definition 13.25 Second fundamental coefficients

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1119 · p. 463

ground object -- no derivation owed

Rests on

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 13.8 Curve ¶
    - depends_on definition 13.18 Surface ¶
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 definition 13.27 Riemann symbols ¶
- depends_on theorem 13.30 Theorema Egregium; Gauss, 1827 ¶ ↺
depends_on proposition A.493 A harmonic conformal map is a minimal surface ¶

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`	→	Second fundamental form	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1124
`depends_on`	→	Unit normal vector of a surface	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1124
`depends_on`	←	Gaussian curvature	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1525
`depends_on`	←	Riemann symbols	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1400
`depends_on`	←	A harmonic conformal map is a minimal surface	declared	appendices/A-long-proofs.tex:24139