(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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!

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# Homework Help: Problem about mean curvature

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