The aboriginal and additional axiological forms of a apparent actuate its important differential-geometric invariants: the Gaussian curvature, the beggarly curvature, and the arch curvatures.
The arch curvatures are the invariants of the brace consisting of the additional and aboriginal axiological forms. They are the roots κ1, κ2 of the boxlike equation
The Gaussian curvature K = κ1κ2 and the beggarly curvature H = 1/2(κ1 + κ2) can be computed as follows:
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