A Riemannian manifold \((M,g)\) is called flat is it locally isometric to \((\mathbb{R}^n, \bar{g})\), where \(\bar{g}\) denotes the euclidean metric .
Remark
- \(g\) is also called flat
- Every 1-dimensional Riemannian manifold is flat.
A Riemannian manifold \((M,g)\) is called flat is it locally isometric to \((\mathbb{R}^n, \bar{g})\), where \(\bar{g}\) denotes the euclidean metric .