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First fundamental form ( $I$ )

The first fundamental form of a surface

S \subseteq R^{3}

is the restriction of the ambient inner product to each tangent space

T_{p} S

. For a parametrized surface

X (u, v)

, it is

I = E d u^{2} + 2 F d u d v + G d v^{2}, E = X_{u}^{2}, F = X_{u} \cdot X_{v}, G = X_{v}^{2} .

Table of contents 184 7
- Local isometry First fundamental form 113 4
- Area element of a surface First fundamental form 38 1
  - Vector area element Area element of a surface 14

 Ancestors (5)

 Incoming links (14)