Some recent developments in differential geometry

@article{White1989SomeRD,
  title={Some recent developments in differential geometry},
  author={Brian White},
  journal={The Mathematical Intelligencer},
  year={1989},
  volume={11},
  pages={41-47}
}
  • B. White
  • Published 1 September 1989
  • Mathematics
  • The Mathematical Intelligencer
Until recently differential geometry was the s tudy of fixed curves or surfaces in space and of abstract manifolds with fixed Riemannian metrics. Now geometers have begun to s tudy curves and surfaces that are subjected to various forces and that flow or evolve with time in response to those forces. Perhaps the simplest example (but already a very subtle one) is the curve-shortening flow. Consider a simple closed curve in the plane, and suppose that it moves so that the velocity at each point… 

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