A surface given by the parametric equations
(1)
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(2)
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(3)
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The handkerchief surface has stationary points summarized in the table below, where the type of point can be found using the second derivative test.
point | |||
48 | local maximum | ||
4 | saddle point |
Its first fundamental form has coefficients
(4)
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(5)
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(6)
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and its second fundamental form has coefficients
(7)
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(8)
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(9)
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The Gaussian curvature can be given implicitly by
(10)
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