definition 13.29 Gaussian curvature

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1519 · p. 468

Rests on

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 13.8 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 definition 13.28 Normal curvature vector of a surface ¶
- 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 13.20 Unit normal vector of a surface ¶
  - depends_on definition 13.19 Parameter curves ¶ ↺
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 13.20 Unit normal vector of a surface ¶ ↺

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`	→	First fundamental coefficients	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1525
`depends_on`	→	Normal curvature vector of a surface	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1525
`depends_on`	→	Second fundamental coefficients	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1525
`depends_on`	←	Theorema Egregium; Gauss, 1827	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:1552