Thanks Luca. I have been looking at tests also.

For CompositionManifold, if

H = CompositionManifold(F, G)

then

H_pullback = F_pullback * G_pullback

H_pushforward = G_pushforward * F_pushforward

I think adding this to documentation will improve the description.

Also this line

dim1 The dimension of the first ChartManifold
<https://www.dealii.org/developer/doxygen/deal.II/classChartManifold.html>,
which coincides also with the chart dimension of the second ChartManifold
<https://www.dealii.org/developer/doxygen/deal.II/classChartManifold.html>

does not seem to be correct in my case

       static const PolarManifold<2,3> sphere;
       static const FunctionManifold<3,3,3> rotate("x;-z;y","x;z;-y");
       static const CompositionManifold<2,3,3,3,2,3> rotated_sphere(sphere,
rotate);

dimension of first manifold (sphere) = 2

but this is not equal to

chart dimension of second manifold (rotate) = 3 ???

Best
praveen

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