- #1

raopeng

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## Homework Statement

Prove that the only surfaces with zero mean curvature are either planes or hyperbolic curves with the equation: [itex]y = \frac{\cosh (ax+b)}{a}[/itex] rotating alone the x axis.

## Homework Equations

## The Attempt at a Solution

I made an attempt by devoting the equation of the surface as r = r(x) then take this back to the definition of mean curvature which ended up with a very complicated differential equation. Then I worked out the expression of mean curvature using Vieta's formula only to find myself facing a even more complex differential equation again. However there must be an easy way to prove the statement.

Thanks!