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Curvatures of an arc-length surface of revolution

With unit normal

(- Z^{'} cos v, - Z^{'} sin v, Y^{'})

, the principal-form coefficients give

K = - \frac{Y ^{''}}{Y}, H = \frac{1}{2} (Y^{'} Z^{''} - Z^{'} Y^{''} + \frac{Z ^{'}}{Y}) .

Table of contents 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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