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Third fundamental form

$\displaystyle \mathbb{III}(\vec{v}, \vec{w}) = W_x(\vec{v})\cdot W_x(\vec{w})$

The third fundamental form is given in terms of the first and second forms by:

$\displaystyle \mathbb{III}- 2H\mathbb{II}+ K\mathbb{I}= 0$

where $ H$ is the mean curvature and $ K$ is the Gaussian curvature.


Alexis Angelidis (PhD) 2004-02-09