Letx:D→E be the map defined by parabolic cylindrical coordinates(u,U,z)∈D,where(u,U)∈R2-{(0,0)},z∈RandEr(u,,)=(-3)1.Find dr and express it as dz=0e+ez+e3,where el,ez,ea is a moving frameon D and 0 h du,h2du,hadz for functions h to be determined.4]2.Compute the connection 1-forms Show that the first and second structure equa-tions are satisfied.6
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