Fundamental Forms of Surfaces and the Gauss-bonnet Theorem

  title={Fundamental Forms of Surfaces and the Gauss-bonnet Theorem},
  author={Hunter S Chase},
  • Hunter S Chase
  • Published 2012
We define the first and second fundamental forms of surfaces, exploring their properties as they relate to measuring arc lengths and areas, identifying isometric surfaces, and finding extrema. These forms can be used to define the Gaussian curvature, which is, unlike the first and second fundamental forms, independent of the parametrization of the surface. Gauss’s Egregious Theorem reveals more about the Gaussian curvature, that it depends only on the first fundamental form and thus identifies… CONTINUE READING

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