embedding problem

winshum · science forum beginner Joined: 22 Aug 2005 Posts: 5

a cylindrically symmetric manifold is described by the line element
ds^2=4e^(2ar)dr^2+r^2d@^2
now the manifold is embedded into 3-D flat space, with Euclidean coordinates x,y,z where
r=sqrt(x^2+y^2)
z=h(r)
Find a differential equation satisfied by h(r)
and also how to solve h(r)
i haven't study differential geometry and it is a problem about general relativity, could anyone gives me any ideas of this problem and also what does "Manifold" really mean? thanks!

Google