It would be great for metric manifolds to work out of the box on LieGroups and call into the base_manifold by default. I couldn't quite figure out how to get a few functions to work (mostly struggled with ambiguities), so ended up overloading:

• hat
• vee
• get_vector
• get_vector!
• get_coordinates
• get_coordinates!
• identity_element

I fully hardcoded identity_element to get rid of ambiguities -- see this comment by @kellertuer in JuliaRobotics/RoME.jl#775 (comment)

in the long run we might best consider making identity_element agnostic of the metric; that is that ou do not have to reimplement that for a new metric.

If some of the functions should already work and I'm doing something wrong, please let me know. In the short term the overloaded functions should work, so not the highest priority.