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An elliptic cylinder is a cylinder with an elliptical cross section.
The elliptic cylinder is a quadratic ruled surface.
The parametric equations for the laterals sides of an elliptic cylinder of height , semimajor axis , and semiminor axis are
(1)
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(2)
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(3)
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where and .
The volume of the elliptic cylinder is
(4)
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The coefficients of the first fundamental form are
(5)
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(6)
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(7)
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and of the second fundamental form are
(8)
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(9)
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(10)
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The area element is
(11)
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The Gaussian and mean curvatures are
(12)
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(13)
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