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Can the theorem be proved invariantly, without any reference to charts,frames, basis vectors or coordinates?

Can the theorem be proved invariantly, without any reference to charts basis vectors or coordinates?

Can the theorem be proved invariantly, without any reference to charts,frames, basis vectors or coordinates?

Post Closed as "Needs details or clarity" by Sean Lawton, abx, YCor, Ivan Izmestiev, Anthony Quas
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YCor
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Coordinate free proof of Gauss Bonet-Bonnet theorem

Can the theorem be proved invariantly  , without any reference to charts basis vectors or coordinates?

Coordinate free proof of Gauss Bonet theorem

Can the theorem be proved invariantly  , without any reference to charts basis vectors or coordinates?

Coordinate free proof of Gauss-Bonnet theorem

Can the theorem be proved invariantly, without any reference to charts basis vectors or coordinates?

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Riu
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Coordinate free proof of Gauss Bonet theorem

Can the theorem be proved invariantly , without any reference to charts basis vectors or coordinates?