Hello
I know that the metric is an intrinsic property of a manifold, hence it should be possible to compute it without any use of an embedding in a higher dimensional space.
That is, one can easily compute the metric on a surface of a 2-sphere just by computing the inner products of the basis tangent vectors as they appear in R^3, with the trivial Euclidean inner product.
My question is, can one compute the metric without recurring to the embedding?
Thank you in advance.
-artur palha