Regular curves on Riemannian manifolds

@article{Smale1958RegularCO,
  title={Regular curves on Riemannian manifolds},
  author={Stephen Smale},
  journal={Transactions of the American Mathematical Society},
  year={1958},
  volume={87},
  pages={492-512}
}
  • S. Smale
  • Published 1 February 1958
  • Mathematics
  • Transactions of the American Mathematical Society
Introduction. A regular curve on a Riemannian manifold is a curve with a continuously turning nontrivial tangent vector.(2) A regular homotopy is a homotopy which at every stage is a regular curve, keeps end points and directions fixed and such that the tangent vector moves continuously with the homotopy. A regular curve is closed if its initial point and tangent coincides with its end point and tangent. In 1937 Hassler Whitney [17] classified the closed regular curves in the plane according to… 
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