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The surface given by the parametric equations
(1)
(2)
(3)
The coefficients of the first fundamental form are
(4)
(5)
(6)
and of the second fundamental form are
(7)
(8)
(9)
The Gaussian and mean curvatures are given by
(10)
(11)
and the principal curvatures are
(12)
(13)
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