Timeline for Gaussian curvature and mean curvature.
Current License: CC BY-SA 2.5
3 events
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| Jun 28, 2011 at 14:49 | comment | added | Fly by Night | If the surface is written as $z = -\frac{1}{2}(ax^2+by^2)+\cdots$ then the usual definition of mean curvature is the mean of the principal curvatures, i.e. $H = \frac{1}{2}(a+b).$ Removing the factor of one half, i.e. setting $H = a + b$ is non-standard and seems to be most prevalent in fluid mechanics. Recall that a surface can be written as $z = \frac{1}{2}(\kappa_1x^2+\kappa_2y^2) + \cdots$ where $\kappa_1$ and $\kappa_2$ are principal curvatures and the $x$-axis and $y$-axis are principal directions. If $\kappa_1 = \kappa_2$ then the point is an umbilic and every direction is principal. | |
| Oct 19, 2009 at 0:32 | history | edited | Deane Yang | CC BY-SA 2.5 |
Fixed formula
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| Oct 18, 2009 at 1:12 | history | answered | Deane Yang | CC BY-SA 2.5 |