Circle (Riemannian manifold): Difference between revisions
(New page: ==Definition== The '''circle''', as a Riemannian manifold, or as an ''intrinsic'' curve, is defined as a simple closed curve (i.e. diffeomorphic to the circle) satisfying the followin...) |
m (1 revision) |
(No difference)
| |
Latest revision as of 19:34, 18 May 2008
Definition
The circle, as a Riemannian manifold, or as an intrinsic curve, is defined as a simple closed curve (i.e. diffeomorphic to the circle) satisfying the following equivalent properties:
- Its curvature is constant, and its torsion is zero
- It can be embedded as a submanifold of the plane, as a circle in the plane.