Fr.: variété plate
A manifold with a → Riemannian metric that has → zero → curvature.
A → topological space in which every point has a → neighborhood which resembles → Euclidean space (Rn), but in which the global structure may be different. An example of a one-dimensional manifold would be a circle; if you zoom around a point the circle looks locally like a line (R1). An example of a two-dimensional manifold would be a sphere; a small portion looks locally like a plane (R2). See also → flat manifold.
O.E. monigfald (Anglian), manigfeald (W.Saxon) "varied in appearance," from manig "many" + -feald "fold."
Baslâ, from bas "many, much" (Mid.Pers. vas "many, much;" O.Pers. vasiy "at will, greatly, utterly;" Av. varəmi "I wish," vasô, vasə "at one's pleasure or will," from vas- "to will, desire, wish") + lâ "fold."
Fr.: variété riemannienne
A → manifold on which there is a defined → Riemannian metric (Douglas N. Clark, 2000, Dictionary of Analysis, Calculus, and Differential Equations).
→ Riemannian; → metric.