Group of matrices form a manifold or euclidean space There is a very interesting question How can a group of matrices form a manifold.  From the answers it looks more like group of matrices form euclidean space than a general manifold. I understand that euclidean space is a manifold, but manifold is very general and has curvature.  My question is what exactly makes a group of matrices a manifold but not simply a euclidean space.


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*I am not a mathematician so please correct me if there is anything wrong with the question or the way I posed it.


In the question to which you refer the group of matrices is given a manifold structure by virtue of its embedding in a Euclidean space. So for example you can think of a torus as a two dimensional manifold (with interesting curvature) by using the differentiable structure it gets from the usual embedding as a curved surface in $3$-space. That doesn't make the torus a Euclidean space.
