The surface with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the torsion.
The coefficients of the first fundamental form are
 |  | ![(a^2[1-tau^2+(1+tau^2)cosh(2v)])/(2(1+coshucoshv)^2)](/images/equations/HyperbolicHelicoid/Inline13.svg) |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
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and those of the second fundamental form are
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  |  |
(9)
|
The Gaussian curvature is a somewhat complicated, but the mean curvature is given by
 |
(10)
|
