Planar curve: Difference between revisions

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(New page: ==Definition== A '''planar curve''' is a one-dimensional connected Riemannian manifold (in other words, a curve) satisfying the following equivalent conditions: * The [[torsion of a curv...)
 
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Latest revision as of 19:50, 18 May 2008

Definition

A planar curve is a one-dimensional connected Riemannian manifold (in other words, a curve) satisfying the following equivalent conditions:

  • The torsion is zero at all points
  • The curve can be embedded as a Riemannian submanifold of the plane: in other words, it can be viewed as a curve in the plane, inheriting the Riemannian metric from the plane