The surface given by the parametric equations
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(1)
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(2)
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(3)
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It is a sextic surface with algebraic equation
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(4)
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The coefficients of the first fundamental form are
 |  | ![a^2[cos^2u+cos^2(u+v)]](/images/equations/SineSurface/Inline12.svg) |
(5)
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(6)
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 |  | ![a^2[cos^2v+cos^2(u+v)],](/images/equations/SineSurface/Inline18.svg) |
(7)
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the second fundamental form coefficients are
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(8)
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(9)
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(10)
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the area element is
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(11)
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the Gaussian curvature is
![K=(cosucosv[sinusinv-cosucosvsin^2(u+v)])/([acos^2ucos^2v+a(cos^2u+cos^2v)cos^2(u+v)]^2),](/images/equations/SineSurface/NumberedEquation3.svg) |
(12)
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and the mean curvature is a complicated expression.
It has volume
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(13)
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