A Riemannian manifold is conformally flat if it is locally taken to a flat manifold by a conformal transformation; more specifically, if there exists an open cover and on each a smooth function , such that has vanishing Riemann curvature: .
See also
Wikipedia, Conformally flat manifold
Michael Kapovich, Conformally flat metrics on 4-manifolds, J. Differential Geom. Volume 66, Number 2 (2004), 289-301 (euclid:1102538612)
Created on May 22, 2019 at 17:33:19. See the history of this page for a list of all contributions to it.