shape operator

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English

Noun

shape operator (plural shape operators)

  1. (geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface.
    • 1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304:
      Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this intrinsic geometry, since it passes the test of isometric invariance.
    • 2006, Balkan Journal of Geometry and Its Applications, volumes 11-12, page 41:
      Timelike surfaces have symmetric shape operators which can be put into one of three canonical forms on a fixed tangent space with respect to an orthonormal basis: [] .
    • 2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85:
      We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal , a zero shape operator for a surface should imply that is a plane. This is verified by the following result.

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