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Yesterday during a lecture the Klein Bottle manifold was mentioned.

We've been busy with describing the natural way of conducting mechanics on manifolds for a while now.

Does anybody know how an example of a mechanical system which is described by a klein bottle manifold? I've been trying to think of one and googling didn't really result in anything. Just mentions of the klein bottle but no examples.

I have read something about a sliding constraint + another one but I can't find it anymore (my bad).

Are this kind of manifolds used in GR as well?

Kind regards,

Joris