nLab
conformally flat manifold

Contents

Contents

Idea

A Riemannian manifold (X,g)(X,g) is conformally flat if it is locally taken to a flat manifold by a conformal transformation; more specifically, if there exists an open cover {U iX} iI\{U_i \to X\}_{i \in I} and on each U iU_i a smooth function f if_i, such that e f ig |U ie^{f_i} g_{\vert U_i} has vanishing Riemann curvature: R(e f ig |U i)=0R\big( e^{f_i} g_{\vert U_i} \big) = 0.

Examples

References

See also

Created on May 22, 2019 at 13:33:19. See the history of this page for a list of all contributions to it.