Dictionary

shape operator en · NOUN

Meanings

1. (qualifier:differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface.
   • 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:[…]. 2006, Balkan Journal of Geometry and Its Applications, volumes 11-12, page 41:
   • 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. 1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304:
   • We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal U, a zero shape operator for a surface M should imply that M is a plane. This is verified by the following result. 2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85:

Forms

Synonyms

Weingarten map (differential of a Gauss map)