- #1
TrickyDicky
- 3,507
- 27
One usually needs multiple local charts to cover a manifold ( no global coordinate system), the manifold in general is covered by local patches with overlapping areas.
But if we embed a certain manifold in a higher dimension space, like for instance embedding a 2-sphere in a Euclidean space, then from this space I guess we can cover the whole original manifold with a global coordinate system. If this was the case, the benefit seems clear, would there be any drawback?
But if we embed a certain manifold in a higher dimension space, like for instance embedding a 2-sphere in a Euclidean space, then from this space I guess we can cover the whole original manifold with a global coordinate system. If this was the case, the benefit seems clear, would there be any drawback?