Umbilic points on Gaussian random surfaces

  title={Umbilic points on Gaussian random surfaces},
  author={Michael V. Berry and J H Hannay},
  journal={Journal of Physics A},
An umbilic point U on a surface Sigma is a place where the two principal curvatures of Sigma are equal. U is a singularity of Sigma in three different senses: (i) it is the source of elliptic (E) or hyperbolic (H) umbilic catastrophes in the envelope of normals ('focal surface') of Sigma ; (ii) it has index +or-1/2 depending on whether the principal curvature directions of Sigma (defining the lines of curvature) rotate by +or- pi during a circuit of U; (iii) it has a pattern of the 'star' (S… 

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