# How can we model intrinsic curvature?

Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?

If a space is a Euclidean space, in the sense that it has a Euclidean metric, then its Levi Civita connection (the connection compatible with its metric) has no intrinsic curvature (for example a flat plane is like this). However, it may be given some extrinsic curvature by means of an embedding into a higher dimensional space (the flat plane may be rolled up into a cylinder in $\mathbb{R}^3$).