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First fundamental form of an arc-length surface of revolution

For

X (u, v) = (Y (u) cos v, Y (u) sin v, Z (u))

with

Y^{'2} + Z^{'2} = 1

, the induced metric is

d u^{2} + Y (u)^{2} d v^{2} .

Table of contents 113 4
- Curvatures of an arc-length surface of revolution First fundamental form of an arc-length surface of revolution 101 3
  - Constant Gaussian curvature surfaces of revolution Curvatures of an arc-length surface of revolution 54
  - Gaussian curvature of a surface of revolution Curvatures of an arc-length surface of revolution 33 1
    - Total Gaussian curvature of a surface-of-revolution strip Gaussian curvature of a surface of revolution 19

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 Incoming links (1)

Solution